on the complexity of finding chordless paths in bipartite graphs and some interval operators in graphs and hypergraphs in this paper we show that the problem of finding a chordless path between a vertex s and a vertex t containing a vertex v remains np complete in bipartite graphs thereby strengthening the previous results on the same problem we show a relation between this problem and two interval operators the simple path interval operator in hypergraphs and the even chorded path interval operator in graphs we show that the problem of computing the two mentioned intervals is np complete

some properties of graphs determined by edge zeta functions in 1989 hashimoto introduced an edge zeta function of a finite graph which is a generalization of the ihara zeta function the edge zeta function is the reciprocal of a polynomial in twice as many indeterminants as edges in the graph and can be computed via a determinant expression we look at graph properties which we can determine using the edge zeta function in particular the edge zeta function is enough to deduce the clique number the number of hamiltonian cycles and whether a graph is perfect or chordal finally we present a new example illustrating that the ihara zeta function cannot necessarily do the same

generalized continuous nondifferentiable fractional programming problems with invexity abstract the concept of invexity has allowed the convexity requirements in a variety of mathematical programming problems to be weakened we extend a number of kuhn tucker type sufficient optimality criteria for a class of continuous nondifferentiable minmax fractional programming problems that involves several ratios in the objective with a nondifferentiable term in the numerators as an application of these optimality results various mond weir type duality results are proved under a variety of generalized invexity assumptions these results extend many well known duality results and also give a dynamic generalization of those of finite dimensional nonlinear programming problems recently explored

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

field theory of directed percolation with long range spreading it is well established that the phase transition between survival and extinction in spreading models with short range interactions is generically associated with the directed percolation dp universality class in many realistic spreading processes however interactions are long ranged and well described by l evy flights char22 i e by a probability distribution that decays in d dimensions with distance r as r ensuremath d ensuremath ensuremath sigma we employ the powerful methods of renormalized field theory to study dp with such long range l evy flight spreading in some depth our results unambiguously corroborate earlier findings that there are four renormalization group fixed points corresponding to respectively short range gaussian l evy gaussian short range and l evy dp and that there are four lines in the ensuremath sigma d plane which separate the stability regions of these fixed points when the stability line between short range dp and l evy dp is crossed all critical exponents change continuously we calculate the exponents describing l evy dp to second order in an ensuremath epsilon expansion and we compare our analytical results to the results of existing numerical simulations furthermore we calculate the leading logarithmic corrections for several dynamical observables

invasion percolation with long range correlations first order phase transition and nonuniversal scaling properties we present the results of extensive monte carlo simulations of the invasion percolation model with trapping tip with long range correlations a problem which is relevant to multiphase flow in field scale porous media such as oil reservoirs and groundwater aquifers as well as flow in rock fractures the correlations are generated by a fractional brownian motion characterized by a hurst exponent h we employ a highly efficient algorithm for simulating tip and a novel method for identifying the backbone of tip clusters both site and bond tip are studied our study indicates that the backbone of bond tip is loopless and completely different from that of site tip we obtain precise estimates for the fractal dimensions of the sample spanning cluster ssc the minimal path and the backbone of site and bond tip and analyze the size distribution of the trapped clusters in order to identify all the possible universality classes of tip with long range correlations for site tip with h 1 2 the ssc and its backbone are compact indicating a first order phase transition at the percolation threshold while the minimal paths are essentially straigth lines for h 1 2 the ssc its backbone and the minimal paths are all fractal with fractal dimensions that depend on the hurst exponent h the fractal dimension of the loopless backbone for bond tip is much less than that of site tip for any h

influence of long range interactions on the critical behavior of systems with a negative fisher exponent the influence of long range interactions decaying in d dimensions as 1 r d sigma on the critical behavior of systems with fisher s correlation function exponent for short range interactions eta sr 0 is re examined such systems typically described by phi 3 field theories are e g the potts model in the percolation limit the edwards anderson spin glass and the yang lee edge singularity in contrast to preceding studies it is shown by means of wilson s momentum shell renormalization group recursion relations that the long range interactions dominate as long as sigma 2 eta sr exponents change continuously to their short range values at the boundary of this region

the fractal dimension of the minimum path in two and three dimensional percolation the authors calculate the fractal dimension d min of the shortest path l between two points on a percolation cluster where l approximately rd min and r is the pythagorean distance between the points they find d min 1 130 or 0 002 for d 2 and 1 34 or 0 01 for d 3

symmetric duality for a class of nondifferentiable multi objective fractional variational problems abstract we introduce a symmetric dual pair for a class of nondifferentiable multi objective fractional variational problems weak strong converse and self duality relations are established under certain invexity assumptions the paper includes extensions of previous symmetric duality results for multi objective fractional variational problems obtained by kim lee and schaible d s kim w j lee s schaible symmetric duality for invex multiobjective fractional variational problems j math anal appl 289 2004 505 521 and symmetric duality results for the static case obtained by yang wang and deng x m yang s y wang x t deng symmetric duality for a class of multiobjective fractional programming problems j math anal appl 274 2002 279 295 to the dynamic case

shortest paths on systems with power law distributed long range connections we discuss shortest path lengths l r on periodic rings of size l supplemented with an average of pl randomly located long range links whose lengths are distributed according to p l approximately l mu using rescaling arguments and numerical simulation on systems of up to 10 7 sites we show that a characteristic length xi exists such that l r approximately r for r xi for small p we find that the shortest path length satisfies the scaling relation l r mu p xi f mu r xi three regions with different asymptotic behaviors are found respectively a mu 2 where theta s 1 b 1 mu 2 where 0 theta s mu 1 2 and c mu 1 where l r behaves logarithmically i e theta s 0 the characteristic length xi is of the form xi approximately p nu with nu 1 2 mu in region b but depends on l as well in region c a directed model of shortest paths is solved and compared with numerical results

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

a combinatorial approach to nonlocality and contextuality so far most of the literature on quantum contextuality and the kochen specker theorem seems either to concern particular examples of contextuality or be considered as quantum logic here we develop a general formalism for contextuality scenarios based on the combinatorics of hypergraphs which significantly refines a similar recent approach by cabello severini and winter csw in contrast to csw we explicitly include the normalization of probabilities which gives us a much finer control over the various sets of probabilistic models like classical quantum and generalized probabilistic in particular our framework specializes to quantum nonlocality in the case of bell scenarios which arise very naturally from a certain product of contextuality scenarios due to foulis and randall in the spirit of csw we find close relationships to several graph invariants the recently proposed local orthogonality principle turns out to be a special case of a general principle for contextuality scenarios related to the shannon capacity of graphs our results imply that it is strictly dominated by a low level of the navascues pironio acin hierarchy of semidefinite programs which we also apply to contextuality scenarios

hybrid tractability of valued constraint problems the constraint satisfaction problem csp is a central generic problem in computer science and artificial intelligence it provides a common framework for many theoretical problems as well as for many real life applications valued constraint problems are a generalisation of the csp which allow the user to model optimisation problems considerable effort has been made in identifying properties which ensure tractability in such problems in this work we initiate the study of hybrid tractability of valued constraint problems that is properties which guarantee tractability of the given valued constraint problem but which do not depend only on the underlying structure of the instance such as being tree structured or only on the types of valued constraints in the instance such as submodularity we present several novel hybrid classes of valued constraint problems in which all unary constraints are allowed which include a machine scheduling problem constraint problems of arbitrary arities with no overlapping nogoods and the softalldiff constraint with arbitrary unary valued constraints an important tool in our investigation will be the notion of forbidden substructures

combinatorial symbolic powers abstract symbolic powers are studied in the combinatorial context of monomial ideals when the ideals are generated by quadratic squarefree monomials the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blowups as a result perfect graphs play an important role in the theory dual to the role played by perfect graphs in the theory of secants of monomial ideals we use grobner degenerations as a tool to reduce questions about symbolic powers of arbitrary ideals to the monomial case among the applications are a new unified approach to the grobner bases of symbolic powers of determinantal and pfaffian ideals

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

first order transition in the one dimensional three state potts model with long range interactions the first order phase transition in the three state potts model with long range interactions decaying as 1 r 1 ensuremath sigma has been examined by numerical simulations using the recently proposed luijten bl ote algorithm by applying scaling arguments to the interface free energy the binder s fourth order cumulant and the specific heat maximum the change in the character of the transition through variation of parameter ensuremath sigma was studied

one dimensional ising models with long range interactions we consider ising models with long range ferromagnetic pair interactions decaying as for we first find approximate values for the critical temperature we use a cluster mean field approach combined with finite size scaling and vanden broeck and schwartz transformations for we find which can be compared with recent results of luijten and blote who found and which is two orders of magnitude more accurate than any previous results since we use a mean field cluster approximation as part of our approach the accuracy for larger values of decreases significantly in addition to we obtain approximate values for the critical exponents and using the coherent anomaly method for we obtain and all extremely close to the predictions of renormalization group calculations which say that these exponents should take on their classical values for this value of

on claw free t perfect graphs a graph is called t perfect if its stable set polytope is defined by non negativity edge and odd cycle inequalities we characterise the class of all claw free t perfect graphs by forbidden t minors and show that they are 3 colourable moreover we determine the chromatic number of claw free h perfect graphs and give a polynomial time algorithm to compute an optimal colouring

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

long range one dimensional potts models a cluster mean field and extrapolation approach we obtain approximations for the critical temperature tc of q state ferromagnetic potts models on one dimensional lattices with algebraically decaying ferromagnetic pair interactions i e decaying as 1 r with 1 2 initially we use a cluster mean field method to get approximations to the critical temperature and we look at increasingly large clusters this gives us a sequence of ever more accurate approximate values which can be used as input to various extrapolation algorithms we see that as the interaction decreases more slowly and the value of q increases we obtain more and more accurate tc estimates our best estimates we believe to be correct to four figure accuracy

characterizing and bounding the imperfection ratio for some classes of graphs perfect graphs constitute a well studied graph class with a rich structure which is reflected by many characterizations with respect to different concepts perfect graphs are for instance precisely those graphs g where the stable set polytope stab g equals the fractional stable set polytope qstab g the dilation ratio rm min t rm qstab g subseteq t rm stab g of the two polytopes yields the imperfection ratio of g it is np hard to compute and for most graph classes it is even unknown whether it is bounded for graphs g such that all facets of stab g are rank constraints associated with antiwebs we characterize the imperfection ratio and bound it by 3 2 outgoing from this result we characterize and bound the imperfection ratio for several graph classes including near bipartite graphs and their complements namely quasi line graphs by means of induced antiwebs and webs respectively

packing and covering with linear programming a survey this paper considers the polyhedral results and the min max results on packing and covering problems of the decade since the strong perfect graph theorem published in 2006 the main such results are available for the packing problem however there are still important polyhedral questions that remain open for the covering problem the main questions are still open although there has been important progress we survey some of the main results with emphasis on those where linear programming and graph theory come together they mainly concern the covering of cycles or dicycles in graphs or signed graphs either with vertices or edges this includes the multicut and integral multiflow problems

percolation in a network with long range connections implications for cytoskeletal structure and function abstract cell shape signaling and integrity depend on cytoskeletal organization in this study we describe the cytoskeleton as a simple network of filamentary proteins links anchored by complex protein structures nodes the structure of this network is regulated by a distance dependent probability of link formation as p p d s where p regulates the network density and s controls how fast the probability for link formation decays with node distance d it was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells here we examined the ability of the two dimensional network to percolate i e to have end to end connectivity and found that the percolation threshold depends strongly on s the system undergoes a transition around s 2 the percolation threshold of networks with s 2 decreases with increasing system size l while the percolation threshold for networks with s 2 converges to a finite value we speculate that s 2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity additionally we measured the length distribution of f actin filaments from publicly available images of a variety of cell types in agreement with model predictions cells originating from more deformable tissues show longer f actin cytoskeletal filaments

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

on the switch markov chain for perfect matchings we study a simple markov chain the switch chain on the set of all perfect matchings in a bipartite graph this markov chain was proposed by diaconis graham and holmes as a possible approach to a sampling problem arising in statistics we ask for which hereditary classes of graphs is the markov chain ergodic and for which is it rapidly mixing we provide a precise answer to the ergodicity question and close bounds on the mixing question we show for the first time that the mixing time of the switch chain is polynomial in the case of monotone graphs a class that includes examples of interest in the statistical setting

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

list matrix partitions of chordal graphs it is well known that a clique with k 1 vertices is the only minimal obstruction to k colourability of chordal graphs a similar result is known for the existence of a cover by l cliques both of these problems are in fact partition problems restricted to chordal graphs the first seeks partitions into k independent sets and the second is equivalent to finding partitions into l cliques in an earlier paper we proved that a chordal graph can be partitioned into k independent sets and l cliques if and only if it does not contain an induced disjoint union of l 1 cliques of size k 1 a linear time algorithm for finding such partitions can be derived from the proof in this paper we expand our focus and consider more general partitions of chordal graphs for each symmetric matrix m over 0 1 the m partition problem seeks a partition of the input graph into independent sets cliques or arbitrary sets with certain pairs of sets being required to have no edges or to have all edges joining them as encoded in the matrix m moreover the vertices of the input chordal graph can be equipped with lists restricting the parts to which a vertex can be placed such list partitions generalize list colourings and list homomorphisms and arise frequently in the theory of graph perfection we show that many m partition problems that are np complete in general become solvable in polynomial time for chordal graphs even in the presence of lists on the other hand we show that there are m partition problems without lists that remain np complete for chordal graphs it is not known whether or not each list m partition problem is np complete or polynomial but it has been shown that each is np complete or quasi polynomial no log n for chordal graphs even this quasi dichotomy is not known but we do identify large families of matrices m for which dichotomy or at least quasi dichotomy holds we also discuss forbidden subgraph characterizations of graphs admitting an m partition such characterizations have recently been investigated for partitions of perfect graphs and we focus on highlighting the improvements one can obtain for the class of chordal rather than just perfect graphs

the complexity of recognizing linear systems with certain integrality properties let a be a 0 1 matrix with precisely two 1 s in each column and let 1 be the all one vector we show that the problems of deciding whether the linear system a bf x ge bf 1 bf x ge bf 0 1 defines an integral polyhedron 2 is totally dual integral tdi and 3 box totally dual integral box tdi are all co np complete thereby confirming the conjecture on np hardness of recognizing tdi systems made by edmonds and giles in 1984

optimality and duality for multiple objective optimization under generalized type i univexity abstract in this paper we extend the classes of generalized type i vector valued functions introduced by aghezzaf and hachimi in j global optim 18 2000 91 101 to generalized univex type i vector valued functions and consider a multiple objective optimization problem involving generalized type i univex functions a number of kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution the mond weir and general mond weir type duality results are also presented

crossover between field theories with short range and long range exchange or correlations the relation between scalar field theories with short range and long range exchange or correlations is studied it is shown to all orders in perturbation theory that the critical exponents of fields and composite operators are continuous functions of the parameters alpha xi characterising the decay rate of the long range exchange correlations with power like falloff 1 rd 2 2 alpha 1 rd 2 xi the scaling law d 2 xi v 2 where v is the correlation length exponent as well as the harris criteria 1970 are shown to be exact to all orders in perturbation theory a discrepancy between two widely used approaches to the crossover problem is pointed out

the complexity of rerouting shortest paths the shortest path reconfiguration problem has as input a graph g with unit edge lengths with vertices s and t and two shortest st paths p and q the question is whether there exists a sequence of shortest st paths that starts with p and ends with q such that subsequent paths differ in only one vertex this is called a rerouting sequence this problem is shown to be pspace complete for claw free graphs and chordal graphs it is shown that the problem can be solved in polynomial time and that shortest rerouting sequences have linear length for these classes it is also shown that deciding whether a rerouting sequence exists between all pairs of shortest st paths can be done in polynomial time finally a polynomial time algorithm for counting the number of isolated paths is given

critical behaviour of the 1d q state potts model with long range interactions the critical behaviour of the one dimensional q state potts model with long range interactions decaying with distance r as r 1 sigma has been studied in the wide range of parameters 0 sigma or 1 and 1 16 or q or 64 a transfer matrix has been constructed for a truncated range of interactions for integer and continuous q and finite range scaling has been applied results for the phase diagram and the correlation length critical exponent are presented

parameterized complexity of vertex deletion into perfect graph classes vertex deletion problems are at the heart of parameterized complexity for a graph class f the f deletion problem takes as input a graph g and an integer k the question is whether it is possible to delete at most k vertices from g such that the resulting graph belongs to f whether perfect deletion is fixed parameter tractable and whether chordal deletion admits a polynomial kernel when parameterized by k have been stated as open questions in previous work we show that perfect deletion and weakly chordal deletion are w 2 hard when parameterized by k in search of positive results we study a restricted variant of the f deletion problem in this restricted variant the deleted vertices must be taken from a specified set x and we parameterize by x we show that for perfect deletion and weakly chordal deletion although this restriction immediately ensures fixed parameter tractability it is not enough to yield polynomial kernels unless np conp poly on the positive side for chordal deletion the restriction enables us to obtain a kernel with o x 4 vertices

yang lee edge singularity in the one dimensional long range ising model the finite range scaling method has been used to study the yang lee edge singularity problem for the one dimensional ferromagnetic ising model with long range interactions decaying with distance r as r d sigma the phase diagram and the critical exponent nu have been calculated for different values of sigma by using finite ranges l or 9 the critical value sigma c dividing the long range from the short range critical regime has been discussed

small world phenomena and the statistics of linear polymers a regular lattice in which the sites can have long range connections at a distance l with a probabilty p l l in addition to the short range nearest neighbour connections shows small world behaviour for 0 c in the most appropriate physical example of such a system namely the linear polymer network the exponent is related to the exponents of the corresponding n vector model in the n 0 limit and its value is less than c still the polymer networks do not show small world behaviour here we show that this is due to a small value constraint on the number q of long range connections per monomer in the network in the general q space we obtain a phase boundary separating regions with and without small world behaviour and show that the polymer network falls marginally in the regular lattice region

effective dimensions in networks with long range connections abstract one and two dimensional lattices of points are connected with long range links whose lengths are distributed according to p r r by changing the decay exponent one can go from d dimensional short range networks to dimensional networks topologically similar to random graphs an effective dimension d chem can be defined in terms of the shortest path properties of these networks these effective dimensions d chem are calculated here in one and two dimensions for system sizes of up to 10 7 points

complexity of independent set reconfigurability problems we study problems of reconfigurability of independent sets in graphs we consider three different models token jumping token sliding and token addition and removal and analyze relationships between them we prove that independent set reconfigurability in perfect graphs under any of the three models generalizes the shortest path reconfigurability problem in general graphs and is therefore pspace complete on the positive side we give polynomial results for even hole free graphs and p 4 free graphs

shortest paths between shortest paths a b s t r a c t we study the following problem on reconfiguring shortest paths in graphs given two shortest s t paths what is the minimum number of steps required to transform one into the other where each intermediate path must also be a shortest s t path and must differ from the previous one by only one vertex we prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is np hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length 2011 elsevier b v all rights reserved

an o nm time certifying algorithm for recognizing hhd free graphs in this paper we consider the recognition problem on a class of perfectly orderable graphs namely the hhd free graphs such graphs do not contain any induced subgraph isomorphic to a house a hole or a domino we prove properties of the hhd free graphs which enable us to present an o nm time and o n m space algorithm for determining whether a graph on n vertices and m edges is hhd free currently this is the fastest algorithm for this problem we also describe how the algorithm can be augmented to provide a certificate an induced house hole or domino whenever it decides that the input graph is not hhd free thus answering an open question posed by hoang and sritharan theoretical computer science 259 2001 233 244 the certificate computation requires o n m additional time and o n space

progress on perfect graphs a graph is perfect if for every induced subgraph the chromatic number is equal to the maximum size of a complete subgraph the class of perfect graphs is important for several reasons for instance many problems of interest in practice but intractable in general can be solved efficiently when restricted to the class of perfect graphs also the question of when a certain class of linear programs always have an integer solution can be answered in terms of perfection of an associated graph

alternatives for testing total dual integrality in this paper we provide characterizing properties of totally dual integral tdi systems among others the following a system of linear inequalities is tdi if and only if its coefficient vectors form a hilbert basis and there exists a test set for the system s dual integer programs where all test vectors have positive entries equal to 1 reformulations of this provide relations between computational algebra and integer programming and they contain applegate cook and mccormick s sufficient condition for the tdi property and sturmfels theorem relating toric initial ideals generated by square free monomials to unimodular triangulations we also study the theoretical and practical efficiency and limits of the characterizations of the tdi property presented here in the particular case of set packing polyhedra our results correspond to endowing the weak perfect graph theorem with an additional computationally interesting geometric feature the normal fan of the stable set polytope of a perfect graph can be refined into a regular triangulation consisting only of unimodular cones

perfectness is an elusive graph property a graph property is called elusive or evasive if every algorithm for testing this property has to read in the worst case n choose 2 entries of the adjacency matrix of the given graph several graph properties have been shown to be elusive e g planarity or k colorability a famous conjecture of karp says that every nontrivial monotone graph property is elusive we prove that a nonmonotone but hereditary graph property is elusive perfectness

reconfiguration of list l 2 1 labelings in a graph for an integer k 0 suppose that each vertex v of a graph g has a set c v 0 1 k of labels called a list of v a list l 2 1 labeling of g is an assignment of a label in c v to each vertex v of g such that every two adjacent vertices receive labels which differ by at least 2 and every two vertices of distance two receive labels which differ by at least 1 in this paper we study the problem of reconfiguring one list l 2 1 labeling of a graph into another list l 2 1 labeling of the same graph by changing only one label assignment at a time while at all times maintaining a list l 2 1 labeling first we show that this decision problem is pspace complete even for bipartite planar graphs and k 6 in contrast we then show that the problem can be solved in linear time for general graphs if k 4 we finally consider the problem restricted to trees and give a sufficient condition for which any two list l 2 1 labelings of a tree can be transformed into each other

on clique separators nearly chordal graphs and the maximum weight stable set problem clique separators in graphs are a helpful tool used by tarjan as a divide and conquer approach for solving various graph problems such as the maximum weight stable set mws problem maximum clique graph coloring and minimum fill in but few examples of graph classes having clique separators are known we use this method to solve mws in polynomial time for two classes where the unweighted maximum stable set ms problem is solvable in polynomial time by augmenting techniques but the complexity of the mws problem was open another example namely a result by alekseev for the mws problem on a subclass of p 5 free graphs obtained by clique separators can be improved by our techniques we also combine clique separators with decomposition by homogeneous sets in graphs and use the following notion a graph is email protected if for each of its vertices the subgraph induced by the set of its nonneighbors has property p we deal with the cases email protected chordal perfect this also simplifies a result obtained by a method called struction

on the complexity of 4 coloring graphs without long induced paths we show that deciding if a graph without induced paths on nine vertices can be colored with 4 colors is an np complete problem improving a previous np completeness result proved by woeginger and sgall in 2001 the complexity of 4 coloring graphs without induced paths on five vertices remains open we show that deciding if a graph without induced paths or cycles on five vertices can be colored with 4 colors can be done in polynomial time a step in our algorithm uses the well known and deep fact due to grotschel lovasz and schrijver stating that perfect graphs can be optimally colored in polynomial time

the connectivity of boolean satisfiability computational and structural dichotomies boolean satisfiability problems are an important benchmark for questions about complexity algorithms heuristics and threshold phenomena recent work on heuristics and the satisfiability threshold has centered around the structure and connectivity of the solution space motivated by this work we study structural and connectivity related properties of the space of solutions of boolean satisfiability problems and establish various dichotomies in schaefer s framework on the structural side we obtain dichotomies for the kinds of subgraphs of the hypercube that can be induced by the solutions of boolean formulas as well as for the diameter of the connected components of the solution space on the computational side we establish dichotomy theorems for the complexity of the connectivity and st connectivity questions for the graph of solutions of boolean formulas our results assert that the intractable side of the computational dichotomies is pspace complete while the tractable side which includes but is not limited to all problems with polynomial time algorithms for satisfiability is in p for the st connectivity question and in conp for the connectivity question the diameter of components can be exponential for the pspace complete cases whereas in all other cases it is linear thus diameter and complexity of the connectivity problems are remarkably aligned the crux of our results is an expressibility theorem showing that in the tractable cases the subgraphs induced by the solution space possess certain good structural properties whereas in the intractable cases the subgraphs can be arbitrary

regular inference as vertex coloring abstract this paper is concerned with the problem of supervised learning of deterministic finite state automata in the technical sense of identification in the limit from complete data by finding a minimal dfa consistent with a sample we solve this problem by translating it in its entirety to a vertex coloring problem essentially such a problem consists of two types of constraints that restrict the hypothesis space inequivalence and equivalence constraints the inequivalence constraints translate to the vertex coloring problem in a very natural way the equivalence constraints however greatly complicate the translation to vertex coloring in previous coloring based translations these were therefore encoded either dynamically by modifying the vertex coloring instance on the fly or by encoding them as satisfiability problems we provide the first translation that encodes both types of constraints together in a pure vertex coloring instance and prove the correctness of the construction the coloring approach offers many opportunities for applying insights from combinatorial optimization and graph theory to regular inference we immediately obtain new complexity bounds as well as a family of new learning algorithms which can be used to obtain exact hypotheses as well as fast approximations we also demonstrate that satisfying all inequivalence constraints in regular inference and vertex coloring are in some sense equally hard this immediately implies that regular inference is not approximable within s 1 s being the cardinality of the sample for any 1 2 unless p np it also indicates that solving only for inequivalence constraints is easier than the full regular inference problem

boundary properties of graphs for algorithmic graph problems the notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature in the present paper we first survey recent results related to this notion and then apply it to two algorithmic graph problems hamiltonian cycle and vertexk colorability in particular we discover the first two boundary classes for the hamiltonian cycle problem and prove that for any k 3 there is a continuum of boundary classes for vertexk colorability

the linear guessing number of undirected graphs abstract this paper investigates linear guessing number introduced by riis in connection with the network coding theory this paper establishes properties of linear guessing number on undirected graphs in particular lower and upper bounds for linear guessing number are established finally linear guessing numbers of product graphs are investigated

crossover from extensive to nonextensive behavior driven by long range d 1 bond percolation abstract we present a monte carlo study of a linear chain d 1 with long range bonds whose occupancy probabilities are given by p ij p r ij 0 p 1 0 where rij 1 2 is the distance between sites the 0 corresponds to the first neighbor mean field particular case we exhibit that the order parameter p equals unity p 0 for 0 1 presents a familiar behavior i e 0 for p pc and finite otherwise for 1 2 our results confirm recent conjecture namely that the nonextensive region 0 1 can be meaningfully unfolded as well as unified with the extensive region 1 by exhibiting p as a function of p where 1 p 1 p n n n 1 d 1 1 d n being the number of sites of the chain a corollary of this conjecture now numerically verified is that pc 1 in the 1 0 limit

discrete sampling a graph theoretic approach to orthogonal interpolation we study the problem of finding unitary submatrices of the n times n discrete fourier transform matrix in the context of interpolating a discrete bandlimited signal using an orthogonal basis this problem is related to a diverse set of questions on idempotents on mathbb z n and tiling mathbb z n in this work we establish a graph theoretic approach and connections to the problem of finding maximum cliques we identify the key properties of these graphs that make the interpolation problem tractable when n is a prime power and we identify the challenges in generalizing to arbitrary n finally we investigate some connections between graph properties and the spectral tile direction of the fuglede conjecture

structural investigation of piecewise linearized network flow problems in this work we study polyhedra in the context of network flow problems in which the flow value on each arc lies in one of several predefined intervals this is motivated by nonlinear problems on transportation networks where nonlinearities are handled by piecewise linear approximation or relaxation a common and established approach in many applications several methods for modeling piecewise linear functions which provide a complete description for a single network arc are known however in general this property is lost when considering multiple arcs we show how to strengthen the formulation for specific substructures consisting of multiple arcs by linear inequalities for the case of paths of degree two nodes we give a complete description of the polyhedron projected to the integer variables our model is based on but not limited to the connection between binary variables and flow variables that is used in the multiple choice method or the convex combination method we also show how to transfe

series analysis of the generalized contact process abstract we study critical behavior in a one parameter family of generalized contact processes using series expansions our results show that the entire family belongs to a single universality class and permit a more accurate assessment of exponent uncertainties

small world networks links with long tailed distributions small world networks swn obtained by randomly adding to a regular structure additional links al are of current interest in this paper we explore based on physical models a new variant of swn in which the probability of realizing an al depends on the chemical distance between the connected sites we assume a power law probability distribution and study random walkers on the network focusing especially on their probability of being at the origin we connect the results to l evy flights which follow from a mean field variant of our model

on the inapproximability of independent domination in 2p3 free perfect graphs we consider the complexity of approximation for the independent dominating set problem in 2p3 free graphs i e graphs that do not contain two disjoint copies of the chordless path on three vertices as an induced subgraph we show that if p np the problem cannot be approximated for 2p3 free graphs in polynomial time within a factor of n1 e for any constant e 0 where n is the number of vertices in the graph moreover we show that the result holds even if the 2p3 free graph is restricted to being weakly chordal and thereby perfect

linear time algorithm for sliding tokens on trees suppose that we are given two independent sets i b and i r of a graph such that i b i r and imagine that a token is placed on each vertex in i b then the sliding token problem is to determine whether there exists a sequence of independent sets which transforms i b into i r so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph this problem is known to be pspace complete even for planar graphs and also for bounded treewidth graphs in this paper we thus study the problem restricted to trees and give the following three results 1 the decision problem is solvable in linear time 2 for a yes instance we can find in quadratic time an actual sequence of independent sets between i b and i r whose length i e the number of token slides is quadratic and 3 there exists an infinite family of instances on paths for which any sequence requires quadratic length

cycle transversals in perfect graphs and cographs a cycle transversal or feedback vertex set of a graph g is a subset t v g such that t v c 0 for every cycle c of g this work considers the problem of finding special cycle transversals in perfect graphs and cographs we prove that finding a minimum cycle transversal t in a perfect graph g is np hard even for bipartite graphs with maximum degree four since g t is acyclic this result implies that finding a maximum acyclic induced subgraph of a perfect graph is also np hard other special properties of t are considered a clique stable respectively cycle transversal or simply cct sct respectively is a cycle transversal which is a clique stable set respectively recognizing graphs which admit a cct can be done in polynomial time however no structural characterization of such graphs is known even for perfect graphs we characterize cographs with cct in terms of forbidden induced subgraphs and describe their structure this leads to linear time recognition of cographs with cct we also prove that deciding whether a perfect graph admits an sct is np complete we characterize cographs with sct in terms of forbidden induced subgraphs this characterization also leads to linear time recognition

msol partitioning problems on graphs of bounded treewidth and clique width we show that a class of vertex partitioning problems that can be expressed in monadic second order logic msol are polynomials on graphs of bounded clique width this class includes coloring h free coloring domatic number and partition into perfect graphs moreover we show that a class of vertex and edge partitioning problems are polynomials on graphs of bounded treewidth

reconfiguration of colorable sets in classes of perfect graphs abstract a set of vertices in a graph is c colorable if the subgraph induced by the set has a proper c coloring in this paper we study the problem of finding a step by step transformation called a reconfiguration sequence between two c colorable sets in the same graph this problem generalizes the well studied independent set reconfiguration problem as the first step toward a systematic understanding of the complexity of this general problem we study the problem on classes of perfect graphs we first focus on interval graphs and give a combinatorial characterization of the distance between two c colorable sets this gives a linear time algorithm for finding an actual shortest reconfiguration sequence for interval graphs since interval graphs are exactly the graphs that are simultaneously chordal and co comparability we then complement the positive result by showing that even deciding reachability is pspace complete for chordal graphs and for co comparability graphs the hardness for chordal graphs holds even for split graphs we also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial time solvable for split graphs but still pspace complete for co comparability graphs the complexity of this case for chordal graphs remains unsettled as by products our positive results give the first polynomial time solvable cases split graphs and interval graphs for feedback vertex set reconfiguration

fixed parameter algorithms for cochromatic number and disjoint rectangle stabbing via iterative localization given a permutation p of 1 n and a positive integer k can p be partitioned into at most k subsequences each of which is either increasing or decreasing we give an algorithm with running time 2 o k 2 l o g k n o 1 that solves this problem thereby showing that it is fixed parameter tractable this np complete problem is equivalent to deciding whether the cochromatic number of a given permutation graph on n vertices is at most k our algorithm solves in fact a more general problem within the mentioned running time it decides whether the cochromatic number of a given perfect graph on n vertices is at most k to obtain our result we use a combination of two well known techniques within parameterized algorithms iterative compression and greedy localization consequently we name this combination iterative localization we further demonstrate the power of this combination by giving an algorithm with running time 2 o k 2 l o g k nlogn that decides whether a given set of n non overlapping axis parallel rectangles can be stabbed by at most k of a given set of horizontal and vertical lines

error correction for index coding with side information a problem of index coding with side information was first considered by birk and kol in 1998 in this study a generalization of index coding scheme where transmitted symbols are subject to errors is studied error correcting methods for such a scheme and their parameters are investigated in particular the following question is discussed given the side information hypergraph of index coding scheme and the maximal number of erroneous symbols what is the shortest length of a linear index code such that every receiver is able to recover the required information this question turns out to be a generalization of the problem of finding a shortest length error correcting code with a prescribed error correcting capability in the classical coding theory the singleton bound and two other bounds referred to as the bound and the bound for the optimal length of a linear error correcting index code ecic are established for large alphabets a construction based on concatenation of an optimal index code with a maximum distance separable classical code is shown to attain the singleton bound for smaller alphabets however this construction may not be optimal a random construction is also analyzed it yields another inexplicit bound on the length of an optimal linear ecic further the problem of error correcting decoding by a linear ecic is studied it is shown that in order to decode correctly the desired symbol the decoder is required to find one of the vectors belonging to an affine space containing the actual error vector the syndrome decoding is shown to produce the correct output if the weight of the error pattern is less or equal to the error correcting capability of the corresponding ecic finally the notion of static ecic which is suitable for use with a family of instances of an index coding problem is introduced several bounds on the length of static ecics are derived and constructions for static ecics are discussed connections of these codes to weakly resilient boolean functions are established

scaling behavior of the contact process in networks with long range connections we present simulation results for the contact process on regular cubic networks that are composed of a one dimensional lattice and a set of long edges with unbounded length networks with different sets of long edges are considered that are characterized by different shortest path dimensions and random walk dimensions we provide numerical evidence that an absorbing phase transition occurs at some finite value of the infection rate and the corresponding dynamical critical exponents depend on the underlying network furthermore the time dependent quantities exhibit log periodic oscillations in agreement with the discrete scale invariance of the networks in case of spreading from an initial active seed the critical exponents are found to depend on the location of the initial seed and break the hyperscaling law of the directed percolation universality class due to the inhomogeneity of the networks however if the cluster spreading quantities are averaged over initial sites the hyperscaling law is restored

on the complexity of reconfiguration problems reconfiguration problems arise when we wish to find a step by step transformation between two feasible solutions of a problem such that all intermediate results are also feasible we demonstrate that a host of reconfiguration problems derived from np complete problems are pspace complete while some are also np hard to approximate in contrast several reconfiguration versions of problems in p are solvable in polynomial time

lovasz schrijver sdp operator near perfect graphs and near bipartite graphs we study the lovasz schrijver lift and project operator mathrm text ls ls based on the cone of symmetric positive semidefinite matrices applied to the fractional stable set polytope of graphs the problem of obtaining a combinatorial characterization of graphs for which the mathrm text ls ls operator generates the stable set polytope in one step has been open since 1990 we call these graphs mathrm text ls ls perfect in the current contribution we pursue a full combinatorial characterization of mathrm text ls ls perfect graphs and make progress towards such a characterization by establishing a new close relationship among mathrm text ls ls perfect graphs near bipartite graphs and a newly introduced concept of full support perfect graphs

index coding with side information motivated by a problem of transmitting supplemental data over broadcast channels birk and kol infocom 1998 we study the following coding problem a sender communicates with n receivers r1 rn he holds an input x 0 01l n and wishes to broadcast a single message so that each receiver ri can recover the bit xi each ri has prior side information about x induced by a directed graph grain nodes ri knows the bits of a in the positions j i j is an edge of g g is known to the sender and to the receivers we call encoding schemes that achieve this goal indexcodes for 0 1 n with side information graph g in this paper we identify a measure on graphs the minrank which exactly characterizes the minimum length of linear and certain types of nonlinear index codes we show that for natural classes of side information graphs including directed acyclic graphs perfect graphs odd holes and odd anti holes minrank is the optimal length of arbitrary index codes for arbitrary index codes and arbitrary graphs we obtain a lower bound in terms of the size of the maximum acyclic induced subgraph this bound holds even for randomized codes but has been shown not to be tight

almost all webs are not rank perfect graphs with circular symmetry called webs are crucial for describing the stable set polytopes of two larger graph classes quasi line graphs 8 12 and claw free graphs 7 8 providing a complete linear description of the stable set polytopes of claw free graphs is a long standing problem 9 ben rebea conjectured a description for quasi line graphs see 12 chudnovsky and seymour 2 verified this conjecture recently for quasi line graphs not belonging to the subclass of fuzzy circular interval graphs and showed that rank facets are required in this case only fuzzy circular interval graphs contain all webs and even the problem of finding all facets of their stable set polytopes is open so far it is only known that stable set polytopes of webs with clique number 3 have rank facets only 5 17 while there are examples with clique number 4 having non rank facets 10 12 15

contraction and deletion blockers for perfect graphs and h free graphs abstract we study the following problem for given integers d k and graph g can we reduce some fixed graph parameter of g by at least d via at most k graph operations from some fixed set s as parameters we take the chromatic number clique number and independence number and as operations we choose edge contraction ec and vertex deletion vd we determine the complexity of this problem for s ec and s vd and for a number of subclasses of perfect graphs we use these results to determine the complexity of the problem for s ec and s vd and restricted to h free graphs

percolation in networks with long range connections abstract two dimensional lattices of points are connected with long range links whose lengths are distributed according to p r r by changing the decay exponent one can go from d dimensional short range networks to dimensional networks topologically similar to random graphs percolation on these networks is numerically studied for systems of up to 10 7 sites the shortest path fractal and chemical dimensions are determined at the critical threshold as a function of the decay exponent

colorings of hypergraphs perfect graphs and associated primes of powers of monomial ideals abstract there is a natural one to one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction let h be a finite simple hypergraph and let j j h be its cover ideal in a polynomial ring r we give an explicit description of all associated primes of r j s for any power j s of j in terms of the coloring properties of hypergraphs arising from h we also give an algebraic method for determining the chromatic number of h proving that it is equivalent to a monomial ideal membership problem involving powers of j our work yields two new purely algebraic characterizations of perfect graphs independent of the strong perfect graph theorem the first characterization is in terms of the sets ass r j s while the second characterization is in terms of the saturated chain condition for associated primes

permanents pfaffian orientations and even directed circuits given a 0 1 square matrix a when can some of the 1 s be changed toi1 s in such a way that the permanent of a equals the determinant of the modifled matrix when does a real square matrix have the property that every real matrix with the same sign pattern that is the corresponding entries either have the same sign or are both zero is nonsingular when is a hypergraph with n vertices and n hyperedges minimally nonbipartite when does a bipartite graph have a pfa an orientation given a digraph does it have no directed circuit of even length given a digraph does it have a subdivision with no even directed circuit it is known that all of the above problems are equivalent we prove a structural characterization of the feasible instances which implies a polynomial time algorithm to solve all of the above problems the structural characterization says roughly speaking that a bipartite graph has a pfa an orientation if and only if it can be obtained by piecing together in a specifled way planar bipartite graphs and one sporadic nonplanar bipartite graph

on algorithms for p 5 gem free graphs a graph is p5 gem free when it does not contain p5 an induced path with five vertices or a gem a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path p4 as an induced subgraph we present o n2 time recognition algorithms for chordal gem free graphs and for p5 gem free graphs using a characterization of p5 gem free graphs by their prime graphs with respect to modular decomposition and their modular decomposition trees a brandstadt d kratsch on the structure of p5 gem free graphs discrete appl math 145 2005 155 166 we give linear time algorithms for the following np complete problems on p5 gem free graphs minimum coloring maximum weight stable set maximum weight clique and minimum clique cover