bluuebunny/crossref_metadata_2025_split huggingface dataset:
Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree
Authors: Niessen Thomas , Volkmann Lutz 
Published: June 2007

AbstractA graph is called Class 1 if the chromatic index equals the maximum degree. We prove sufficient conditions for simple graphs to be Class 1. Using these conditions we improve results on some edge‐coloring theorems of Chetwynd and Hilton. We also improve a theorem concerning the 1‐factorization of regular graphs of high degree.
Diameters of iterated clique graphs of chordal graphs
Authors: Chen Bor‐Liang , Lih Ko‐Wei 
Published: June 2007

AbstractThe clique graph K(G) of a graph is the intersection graph of maximal cliques of G. The iterated clique graph Kn(G) is inductively defined as K(Kn−1(G)) and K1(G) = K(G). Let the diameter diam(G) be the greatest distance between all pairs of vertices of G. We show that diam(Kn(G)) = diam(G) — n if G is a connected chordal graph and n ≤ diam(G). This generalizes a similar result for time graphs by Bruce Hedman.
Vertex signatures and edge‐4‐colorings of 4‐regular plane graphs
Authors: Jaeger François , Koester Gerhard 
Published: June 2007

AbstractWe associate partitions of the edge‐set of a 4‐regular plane graph into 1‐factors or 2‐factors to certain 3‐valued vertex signatures in the spirit of the work by H. Grötzsch [1]. As a corollary we obtain a simple proof of a result of F. Jaeger and H. Shank [2] on the edge‐4‐colorability of 4‐regular plane graphs made up by the superposition of 4 families of disjoint simple closed curves.
Lower bounds for lower Ramsey numbers
Authors: Faudree Ralph , Gould Ronald J. , Jacobson Michael S. , Lesniak Linda 
Published: June 2007

AbstractFor any graph G, let i(G) and μ;(G) denote the smallest number of vertices in a maximal independent set and maximal clique, respectively. For positive integers m and n, the lower Ramsey number s(m, n) is the largest integer p so that every graph of order p has i(G) ≤ m or μ;(G) ≤ n. In this paper we give several new lower bounds for s (m, n) as well as determine precisely the values s(1, n).
On the cycle‐isomorphism of graphs
Authors: Yu Xingxing 
Published: June 2007

AbstractThis paper considers conditions ensuring that cycle‐isomorphic graphs are isomorphic. Graphs of connectivity ⩾ 2 that have no loops were studied in [2] and [4]. Here we characterize all graphs G of connectivity 1 such that every graph that is cycle‐isomorphic to G is also isomorphic to G.
On the residue of a graph
Authors: Favaron O. , Mahéo M. , Saclé J.‐F. 
Published: June 2007

AbstractThe residue R of a simple graph G of degree sequence S: d1 ⩾ d2 ⩾ …︁ ⩾ dn is the number of zeros obtained by the iterative process consisting of deleting the first term d1 of S, subtracting 1 from the d1 following ones, and sorting down the new sequence. The depth is the number n ‐ R of steps in this algorithm. We prove here some conjectures given by the computer program GRAFFITI, in particular, magnified image.
A characterization of domination perfect graphs
Authors: Zverovich I. E. , Zverovich V. E. 
Published: June 2007

AbstractLet γ(G) and i(G) be the domination number and independent domination number of a graph G, respectively. Sumner and Moore [8] define a graph G to be domination perfect if γ(H) = i(H), for every induced subgraph H of G. In this article, we give a finite forbidden induced subgraph characterization of domination perfect graphs.Bollobás and Cockayne [4] proved an inequality relating γ(G) and i(G) for the class of K1,k ‐free graphs. It is shown that the same inequality holds for a wider class of graphs.
[a,b]‐factorizations of graphs
Authors: Mao‐Cheng Cai 
Published: June 2007

AbstractLet a and b be integers with b ⩾ a ⩾ 0. A graph G is called an [a,b]‐graph if a ⩽ dG(v) ⩽ b for each vertex v ∈ V(G), and an [a,b]‐factor of a graph G is a spanning [a,b]‐subgraph of G. A graph is [a,b]‐factorable if its edges can be decomposed into [a,b]‐factors. The purpose of this paper is to prove the following three theorems: (i) if 1 ⩽ b ⩽ 2a, every [(12a + 2)m + 2an,(12b + 4)m + 2bn]‐graph is [2a, 2b + 1]‐factorable; (ii) if b ⩽ 2a −1, every [(12a −4)m + 2an, (12b −2)m + 2bn]‐graph is [2a −1,2b]‐factorable; and (iii) if b ⩽ 2a −1, every [(6a −2)m + 2an, (6b + 2)m + 2bn]‐graph is [2a −1,2b + 1]‐factorable, where m and n are nonnegative integers. They generalize some [a,b]‐factorization results of Akiyama and Kano [3], Kano [6], and Era [5].
Characterization of a class of triangle‐free graphs with a certain adjacency property
Authors: Alspach Brian , Chen C. C. , Heinrich Katherine 
Published: June 2007

AbstractLet m and n be nonnegative integers. Denote by P(m,n) the set of all triangle‐free graphs G such that for any independent m‐subset M and any n‐subset N of V(G) with M ∩ N = Ø, there exists a unique vertex of G that is adjacent to each vertex in M and nonadjacent to any vertex in N. We prove that if m ⩾ 2 and n ⩾ 1, then P(m,n) = Ø whenever m ⩽ n, and P(m,n) = {Km,n+1} whenever m > n. We also have P(1,1) = {C5} and P(1,n) = Ø for n ⩾ 2. In the degenerate cases, the class P(0,n) is completely determined, whereas the class P(m,0), which is most interesting, being rich in graphs, is partially determined.
On the orientable genus of graphs embedded in the klein bottle
Authors: Robertson Neil , Thomas Robin 
Published: June 2007

AbstractLet G be a graph embedded in the Klein bottle with “representativity” at least four. We give a formula for the orientable genus of G, which also implies a polynomially bounded algorithm. The formula is in terms of the number of times certain closed curves on the Klein bottle intersect the graph. In particular, it shows that a cut‐and‐paste technique for re‐embedding graphs is the best possible.
The prism‐free planar graphs and their cycles bases
Authors: Hartvigsen David , Mardon Russell 
Published: June 2007

AbstractDirac (1962) showed that the planar graphs with no prism minor are the graphs obtainable by 2‐sums from bonds, cycles, wheels and K5&&num;92;e's. We give a new characterization of these graphs in terms of an optimization problem defined on the cycle bases of a graph.
On zero‐sum delta‐systems and multiple copies of hypergraphs
Authors: Caro Yair 
Published: June 2007

AbstractWe prove the following generalization of earlier results of Bialostocki and Dierker [3] and Caro [7].Theorem. Let t ⩾ k ⩾ 2 be positive integers such that k | t, and let c :E(K) → ℤk be a mapping of all the r‐subsets of an rt + k −1 element set into the cyclic group of order k; then there are t pairwise disjoint r‐subsets e1, e2, …, et such that Σ c(ei) = 0. This theorem is further generalized to Δ‐systems. An application of this theorem and extension of the proof technique are combined to establish the currently best estimates of the zero‐sum Ramsey numbers R(tG, ℤt).
Upper bounds for harmonious colorings
Authors: McDiarmid Colin , Xinhua Luo 
Published: June 2007

AbstractA harmonious coloring of a simple graph G is a coloring of the vertices such that adjacent vertices receive distinct colors and each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We improve an upper bound on h(G) due to Lee and Mitchem, and give upper bounds for related quantities.
The number of shortest cycles and the chromatic uniqueness of a graph
Authors: Teo C. P. , Koh K. M. 
Published: June 2007

AbstractFor a graph G, let g(G) and σg(G) denote, respectively, the girth of G and the number of cycles of length g(G) in G. In this paper, we first obtain an upper bound for σg(G) and determine the structure of a 2‐connected graph G when σg(G) attains the bound. These extremal graphs are then more‐or‐less classified, but one case leads to an unsolved problem. The structural results are finally applied to show that certain families of graphs are chromatically unique.
Ramsey problems and their connection to tuŕan‐type extremal problems
Authors: Faudree Ralph J. , Simonovits Miklós 
Published: June 2007

AbstractWe shall investigate the behavior of the Ramsey function r(L, Tn), where L is a fixed graph and Tn is a tree on n vertices, while n ← ∞. We prove that in this case the appropriate Ramsey problem can be reduced to a corresponding Turán type extremal problem: if we take a maximum N for which a KN can be colored in two colors so that the first color contains no L and the second color contains no Tn, then by the results of Erdös, Faudree, Rousseau and Schelp, N = (p ‐ 1)n + 0(n), where p is the chromatic number of L. We shall prove that in the corresponding Ramsey‐coloring the edges of the first color from an “almost Turán graph” on p ‐ 1 classes. We shall also describe how the finer structure of L influences this Ramsey number and the stability of the Ramsey coloring. The most important new results—compared with some earlier results—are that we can guarantee structural properties of the extremal colorings.
The value of the Ramsey number r(3, 8)
Authors: McKay Brendan D. , Min Zhang Ke 
Published: June 2007

AbstractThe Ramsey number R(3, 8) can be defined as the least number n such that every graph on n vertices contains either a triangle or an independent set of size 8. With the help of a substantial amount of computation, we prove that R(3, 8)=28.
Hamiltonian graphs involving distances
Authors: Chen Guantao , Schelp R. H. 
Published: June 2007

AbstractLet G be a graph of order n. We show that if G is a 2‐connected graph and max{d(u), d(v)} + |N(u) U N(v)| ≥ n for each pair of vertices u, v at distance two, then either G is hamiltonian or G 3Kn/3 U T1 U T2, where n  O (mod 3), and T1 and T2 are the edge sets of two vertex disjoint triangles containing exactly one vertex from each Kn/3. This result generalizes both Fan's and Lindquester's results as well as several others.
A degree condition for the existence of k‐factors
Authors: Nishimura Tsuyoshi 
Published: June 2007

AbstractLet k be an integer such that ≦, and let G be a connected graph of order n with ≦, kn even, and minimum degree at least k. We prove that if G satisfies max(deg(u), deg(v)) ≦ n/2 for each pair of nonadjacent vertices u, v in G, then G has a k‐factor.
On the number of list‐colorings
Authors: Donner Quentin 
Published: June 2007

AbstractGiven a list of boxes L for a graph G (each vertex is assigned a finite set of colors that we call a box), we denote by f(G, L) the number of L‐colorings of G (each vertex must be colored wiht a color of its box). In the case where all the boxes are identical and of size k, f(G, L) = p(G, k), where P=G, k) is the chromatic polynominal of G.We denote by F(G, k) the minimum of f(G, L) over all the lists of boxes such that each box has size at least k. It is clear that F(G, k) ≤ P(G, k) for all G, k, and we will see in the introduction some examples of graphs such that F(G, k) < P(G, k) for some k. However, we will show, in answer to a problem proposed by A. Kostochka and A. Sidorenko (Fourth Czechoslovak Symposium on Combinatorics, Prachatice, Jin, 1990), that for all G, F(G, k) = P(G, k) for all k sufficiently large. It will follow in particular that F(G, k) is not given by a polynominal in k for all G. The proof is based on the analysis of an algorithm for computing f(G, L) analogous to the classical one for computing P(G, k).
On the minimum size of tight hypergraphs
Authors: Arocha Jorge L. , Bracho Javier , Neumann‐Lara Victor 
Published: June 2007

AbstractA k‐graph, H = (V, E), is tight if for every surjective mapping f: V → {1,….k} there exists an edge α ϵ E sicj tjat f|α is injective. Clearly, 2‐graphs are tight if and only if they are connected. Bounds for the minimum number ϕ of edges in a tight k‐graph with n vertices are given. We conjecture that ϕ for every n and prove the equality when 2n + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow. © 1992 John Wiley & Sons, Inc.
Complete subgraphs with large degree sums
Authors: Faudree Ralph J. 
Published: June 2007

AbstractLet t(n, k) denote the Turán number—the maximum number of edges in a graph on n vertices that does not contain a complete graph Kk+1. It is shown that if G is a graph on n vertices with n ≥ k2(k – 1)/4 and m < t(n, k) edges, then G contains a complete subgraph Kk such that the sum of the degrees of the vertices is at least 2km/n. This result is sharp in an asymptotic sense in that the sum of the degrees of the vertices of Kk is not in general larger, and if the number of edges in G is at most t(n, k) – ϵ (for an appropriate ϵ), then the conclusion is not in general true. © 1992 John Wiley & Sons, Inc.
Vertex 2‐isomorphism
Authors: Swaminathan R. , Wagner Donald K. 
Published: June 2007

AbstractWhitney's theorem on 2‐isomorphism characterizes the set of graphs having the same cycles as a given graph, where a cycle is regarded as a set of edges. In this paper, vertex 2‐isomorphism is defined and used to prove a vertex analogue of Whitney's theorem. The main theorem states that two connected graphs have the same set of cycles, where a cycle is now regarded as a set of vertices, if and only if one can be obtained from the other by a sequence of simple operations. © 1992 John Wiley & Sons, Inc.
On three zero‐sum Ramsey‐type problems
Authors: Alon Noga , Caro Yair 
Published: June 2007

AbstractFor a graph G whose number of edges is divisible by k, let R(G,Zk) denote the minimum integer r such that for every function f: E(Kr) ↦ Zk there is a copy G1 of G in Kr so that Σe∈E(G1) f(e) = 0 (in Zk). We prove that for every integer k1 R(Kn, Zk) ≤ n + O(k3 log k) provided n is sufficiently large as a function of k and k divides (). If, in addition, k is an odd prime‐power then R(Kn, Zk) ≤ n + 2k ‐ 2 and this is tight if k is a prime that divides n. A related result is obtained for hypergraphs. It is further shown that for every graph G on n vertices with an even number of edges R(G,Z2) ≤ n + 2. This estimate is sharp. © 1993 John Wiley & Sons, Inc.
Recombinant DNA in meat additives: Specific detection of Roundup Ready™ soybean by nested PCR
Authors: Brod Fábio CA , Arisi Ana CM 
Published: June 2007

AbstractSoybean proteins are widely used by the meat industry as technological coadjutor when producing processed products such as emulsified and ground meat products. Since regulations for the use and labeling of GMOs and derived ingredients are in force in Brazil, a PCR‐based method capable of detecting Roundup Ready™ (RR) soybean was employed for meat additives. Thirty‐two samples of meat additives containing soy proteins were tested for the presence of soybean amplifiable DNA and RR soybean DNA. Twenty‐five samples gave a positive signal for the lectin gene, confirming the presence of soybean amplifiable DNA and 15 samples returned a positive signal for specific RR detection confirming the presence of genetically modified soy. These results demonstrate for the first time the presence of RR soybean in meat additives. This method may be useful for meat industries interested in controlling the presence of RR soybean in additives used for meat products manufacture. Copyright © 2007 Society of Chemical Industry
Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings
Authors: Elsharkawy Abdallah A. 
Published: June 2007

AbstractConical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman‐extended Darcy equations are utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry and non‐Newtonian behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.
The recent spolis raid in washington
Authors: Marsh H. W. 
Published: June 2007

Abstract“When we see a lot of framed timbers, different portions of which we know to have been gotten out at different times and places by different workmen, Stephen, Franklin, Rogre and James, for instance, and we see all these timbers joined together and see that they exactly make the frame of a house … we find it impossible not to believe that Stephen and Franklin and Roger and James all understood one another from the beginning.”—Abraham Lincoln.
Commentary upon the comparative tax rates of 177 cities, 1923
Authors: Rightor C. E. 
Published: June 2007

AbstractOne year ago (December, 1922) the “Review” published a tabulation of the 1922 tax rates of 32 cities in the United States and Canada, giving the rates in detail by purpose and the total rate adjusted upon a uniform basis for comparison. This year, the Detroit Bureau of Governmental Research, in collecting and tabulating the 1923 tax rates, has expanded the list ot include 165 cities of the United States and 12 cities of Canada having in excess of 30,000 population
Candidate antigens specifically detected by cerebrospinal fluid‐IgG in oligoclonal IgG bands‐positive multiple sclerosis patients
Authors: Nakamura Masashi , Kuramasu Atsuo , Nakashima Ichiro , Fujihara Kazuo , Itoyama Yasuto 
Published: June 2007

AbstractThe aim of the present study was to detect antigenic proteins that react specifically with cerebrospinal fluid (CSF)‐IgG from oligoclonal IgG bands (OB)‐positive multiple sclerosis (MS) patients. To identify such antigenic proteins, we developed a rat brain proteome map using 2‐DE and applied it to the immunoscreening of brain proteins that react with CSF‐IgG but not with serum‐IgG in OB‐positive MS patients. After sequential MALDI‐TOF mass spectrometry, eight proteins [two neuronal proteins (tubulin β‐2 and γ enolase‐2), HSP‐1, Tpi‐1 protein and cellular enzymes (creatine kinase, phosphopyruvate hydratase, triosephosphate isomerase and phosphoglycerate kinase‐1)] were identified as candidate antigens in seven MS patients. Reactivity to tubulin was seen in Western blotting in four patients, and CSF‐specific anti‐tubulin IgG was detected in one patient. In addition, CSF‐specific anti‐gamma enolase IgG was found in another patient. These findings suggest that intrathecal immune responses may occur against a broad range of proteins in MS.
Design and synthesis of cationic Aib‐containing antimicrobial peptides: conformational and biological studies
Authors: Zikou Sofia , Koukkou Anna‐Irini , Mastora Panorea , Sakarellos‐Daitsiotis Maria , Sakarellos Constantinos , Drainas Constantin , Panou‐Pomonis Eygenia 
Published: June 2007

AbstractDevelopment of antimicrobial peptides has attracted considerable attention in recent years due to the excessive use of antibiotics, which has led to multiresistant bacteria. Cationic amphiphilic Aib‐containing peptide models Ac‐(Aib‐Arg‐Aib‐Leu)n‐NH2, n = 1–4, and sequential cationic polypeptides (Arg‐X‐Gly)n, X = Ala, Val, Leu, were prepared and studied for their antimicrobial and hemolytic activity, as well as for their proteolytic stability. Ac‐(Aib‐Arg‐Aib‐Leu)n‐NH2, n = 2, 3 and the polypeptide (Arg‐Leu‐Gly)n exhibited significant antimicrobial activity, and they were nontoxic at their MIC values and resistant, in particular the Aib‐peptide models, to enzymatic degradation. The conformational characteristics of the peptide models were studied by circular dichroism (CD). Structure‐activity relationship studies revealed the importance of the amphipathic α‐helical conformation of the reported peptides in inducing antimicrobial effects. It is concluded that peptide models comprising cationic amino acids (Arg), helicogenic and noncoding residues (Aib) and/or hydrophobic and helix‐promoting components (Leu) may lead to the development of antimicrobial therapeutics. Copyright © 2007 European Peptide Society and John Wiley & Sons, Ltd.
The construction of multi‐factor crossover designs in animal husbandry studies
Authors: Bate S.T. , Boxall J. 
Published: June 2007

AbstractFor ethical reasons it is important to try to obtain as much useful information as possible from an animal experiment whilst minimizing the number of animals used. Crossover designs, where applicable, provide an ideal framework for achieving this. If two or more treatment factors are included in the crossover design then the reduction in total animal usage can be considerable. In this paper we consider such designs, defined as multi‐factor crossover designs. The designs are applicable when there are several different treatment factors, each attlevels, to be applied to the experimental units. The motivation for investigating these designs was a study conducted at GlaxoSmithKline to determine the preference of male and female dogs fort=5 different types of bed andt=5 different bedding conditions. A construction method is given for forming universally optimal designs fortnot too large. Also given is an example for the special case where the number of treatment levelst=6. Copyright © 2007 John Wiley & Sons, Ltd.
The changes of magnetic properties of the perovskite‐type titanium oxides by the structural distortions: In the case of LaTiO3 and YTiO3
Authors: Onishi Taku 
Published: June 2007

AbstractIn the perovskite‐type titanium oxides, the changes of magnetic properties by GdFeO3‐type lattice distortion are observed. In this study, we have performed cluster model calculations based on the density functional theory method, and have obtained the effective exchange integral (Jab) in order to elucidate the magnetic change by the GdFeO3‐type lattice distortion. The components of deciding the orbital ordering and magnetic property have also been discussed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007