bluuebunny/crossref_metadata_2025_split huggingface dataset:
When the cartesian product of two directed cycles is hyperhamiltonian
Authors: Gallian Joseph A. , Witte David 
Published: June 2007

AbstractWe say a digraph G is hyperhamiltonian if there is a spanning closed walk in G which passes through one vertex exactly twice and all others exactly once. We show the cartesian product Za × Zb of two directed cycles is hyperhamiltonian if and only if there are positive integers m and n with ma + nb = ab + 1 and gcd(m, n) = 1 or 2. We obtain a similar result for the vertex‐deleted subdigraphs of Za × Zb.
Edge‐transitive planar graphs
Authors: Grünbaum Branko , Shephard G. C. 
Published: June 2007

AbstractGraphs which are more or less “symmetric” in one sense or another have been the subject of many investigations. In particular, finite graphs in which all edges are equivalent under isomorphisms of the graph have attracted some attention (see, for example, Fleischner and Imrich [2], Grünbaum and Shephard [5]). Here we extend this investigation to infinite planar graphs which are “reasonable” in the sense that they have locally‐finite plane embeddings. The purpose of this paper is to give a complete enumeration of such graphs, both finite and infinite.We remark that the seemingly similar problem of determining all planar graphs in which the vertices are equivalent under isomorphisms of the graph appears to be much harder, and at present we are very far from a solution.
Pancyclic and panconnected line graphs
Authors: Benhocine Abdelhamid , Fouquet Jean‐Luc 
Published: June 2007

AbstractLet G be a graph of order n ⩾ 3. We prove that if G is k‐connected (k ⩾ 2) and the degree sum of k + 1 mutually independent vertices of G is greater than 1/3(k + 1)(n + 1), then the line graph L(G) of G is pancyclic. We also prove that if G is such that the degree sum of every 2 adjacent vertices is at least n, then L(G) is panconnected with some exceptions.
Minimal extensions of graphs to absolute retracts
Authors: Pesch Erwin 
Published: June 2007

AbstractA graph H is an absolute retract if for every isometric embedding h of, into a graph G an edge‐preserving map g from G to H exists such that g · h is the identity map on H. A vertex v is embeddable in a graph G if G − v is a retract of G. An absolute retract is uniquely determined by its set of embeddable vertices. We may regard this set as a metric space. We also prove that a graph (finite metric space with integral distance) can be isometrically embedded into only one smallest absolute retract (injective hull). All graphs in this paper are finite, connected, and without multiple edges.
Homomorphisms of graphs into odd cycles
Authors: Gerards A. M. H. 
Published: June 2007

AbstractWe give a class of graphs G for which there exists a homomorphism (= adjacency preserving map) from V(G) to V(C), where C is the shortest odd cycle in G, thereby extending a result of Albertson, Catlin, and Gibbons. Our class of graphs is characterized by the following property: For each odd subdivision G′ of G there exists a homomorphic map from V(G′) to V(C), where C′ is the shortest odd cycle of G′.
Hamiltonian properties of the cube of a 2‐edge connected graph
Authors: Paoli M. 
Published: June 2007

AbstractLet G be a 2‐edge connected graph with at least 5 vertices. For any given vertices a, b, c, and d in G with a ≠ b, there exists in G3 a hamiltonian path with endpoints a and b avoiding the edge cd, and there exists in G3 ∪ {cd} a hamiltonian path with endpoints a and b and containing the edge cd. Also, after removal of two edges or one edge and one vertex from G3, the resulting graph is still hamiltonian.
A lower bound on the number of spanning trees with k end‐vertices
Authors: Heinrich Katherine , Liu Guizhen 
Published: June 2007

AbstractIf a graph G with cycle rank ρ contains both spanning trees with m and with n end‐vertices, m < n, then G has at least 2ρ spanning trees with k end‐vertices for each integer k, m < k < n. Moreover, the lower bound of 2ρ is best possible.
Exotic n‐universal graphs
Authors: Parsons T. D. , Pisanski Tomaž 
Published: June 2007

AbstractAn n‐universal graph is a graph that contains as an induced subgraph a copy of every graph on n vertices. It is shown that for each positive integer n > 1 there exists an n‐universal graph G on 4n ‐ 1 vertices such that G is a (v, k, λ)‐graph, and both G and its complement G¯ are 1‐transitive in the sense of W. T. Tutte and are of diameter 2. The automorphism group of G is a transitive rank 3 permutation group, i.e., it acts transitively on (1) the vertices of G, (2) the ordered pairs uv of adjacent vertices of G, and (3) the ordered pairs xy of nonadjacent vertices of G.
Nowhere‐zero flows in low genus graphs
Authors: Möller Martina , Carstens Hans Georg , Brinkmann Gunnar 
Published: June 2007

AbstractA nowhere‐zero k‐flow is an assignment of edge directions and integer weights in the range 1,…, k − 1 to the edges of an undirected graph such that at every vertex the flow in is equal to the flow out. Tutte has conjectured that every bridgeless graph has a nowhere‐zero 5‐flow. We show that a counterexample to this conjecture, minimal in the class of graphs embedded in a surface of fixed genus, has no face‐boundary of length <7. Moreover, in order to prove or disprove Tutte's conjecture for graphs of fixed genus γ, one has to check graphs of order at most 28(γ − 1) in the orientable case and 14(γ − 2) in the nonorientable case. So, in particular, it follows immediately that every bridgeless graph of orientable genus ⩽1 or nonorientable genus ⩽2 has a nowhere‐zero 5‐flow. Using a computer, we checked that all graphs of orientable genus ⩽2 or nonorientable genus ⩽4 have a nowhere‐zero 5‐flow.
Chromaticity of triangulated graphs
Authors: Vaderlind Paul 
Published: June 2007

AbstractIt is shown here that a connected graph G without subgraphs isomorphic to K4 is triangulated if and only if its chromatic polynomial P(G,λ) equals λ(λ − 1)m(λ − 2)r for some integers m ≧ 1, r ≧ 0. This result generalizes the characterization of Two‐Trees given by E.G. Whitehead [“Chromaticity of Two‐Trees,” Journal of Graph Theory 9 (1985) 279–284].
Degree sum for a triangle in a graph
Authors: Fan Genghua 
Published: June 2007

AbstractLet 𝒢(n; e) denote the class of graphs on n vertices and e edges. Define f(n, e) = min max{Σ d(vi):{v1, v2,v3} induces a triangle in G}, where the maximum is taken over all triangles in the graph G and the minimum is taken over all G in 𝒢(n; e). From Turán's theorem, f(n, e) = 0 if e ⩽ n2/4; otherwise f(n,e) > 0. Bollobás and Erdös [1] asked to determine the function f(n,e) for e > n2/4. Edwards [3] proved that f(n,e) ⩾ 6e/n for e ≥ n2/3. In this paper, we consider the remaining case, namely, n2/4 < e < n2/3. A construction described in [4] shows that f(n,e) < 4 √3¯e ‐ 2n + 5. We prove that f(n,e) ≥ 21e/4n. In particular, f(n, ⌊n2/4⌋ + 1) > 21n/16, which improves a result of Erdös and Laskar [4] that f(n, ⌊n2/4⌋ + 1) > (1 + ε)n for some positive constant ε. Furthermore, if e ⩾ 0.26n2, we obtain a better result.
On the parity of crossing numbers
Authors: Archdeacon Dan , Richter R. Bruce 
Published: June 2007

AbstractFor an integer n ⩾ 1, a graph G has an n‐constant crossing number if, for any two good drawings ϕ and ϕ′ of G in the plane, μ(ϕ) ≡ μ(ϕ′) (mod n), where μ(ϕ) is the number of crossings in ϕ. We prove that, except for trivial cases, a graph G has n‐constant crossing number if and only if n = 2 and G is either Kp or Kq,r, where p, q, and r are odd.
On feedback vertex sets and nonseparating independent sets in cubic graphs
Authors: Speckenmeyer Ewald 
Published: June 2007

AbstractLet G be an undirected connected graph with n nodes. A subset F of nodes of G is a feedback vertex set (fvs) if G − F is a forest and a subset J of nodes of G is a nonseparating independent set (nsis) if no two nodes of J are adjacent and G − J is connected. f(G), z(G) denote the cardinalities of a minimum fvs and a maximum nsis, respectively, of G. The equation f(G) = n/2 − z(G) + 1 and two new upper bounds on f(G) are derived for cubic graphs G.
A result on Hamiltonian line graphs involving restrictions on induced subgraphs
Authors: Veldman H. J. 
Published: June 2007

AbstractIt is shown that the existence of a Hamilton cycle in the line graph of a graph G can be ensured by imposing certain restrictions on certain induced subgraphs of G. Thereby a number of known results on hamiltonian line graphs are improved, including the earliest results in terms of vertex degrees. One particular consequence is that every graph of diameter 2 and order at least 4 has a hamiltonian line graph.
On connectivities of tree graphs
Authors: Liu Guizhen 
Published: June 2007

AbstractLet T(G) be the tree graph of a graph G with cycle rank r. Then κ(T(G)) ⩾ m(G) − r, where κ(T(G)) and m(G) denote the connectivity of T(G) and the length of a minimum cycle basis for G, respectively. Moreover, the lower bound of m(G) − r is best possible.
An 11‐vertex theorem for 3‐connected cubic graphs
Authors: Aldred R. E. L. , BauSheng  , Holton D. A. , Royle Gordon F. 
Published: June 2007

AbstractIn this paper we determine the circumstances under which a set of 11 vertices in a 3‐connected cubic graph lies on a cycle. In addition, we consider the number of such cycles that exist and characterize those graphs in which a set of 9 vertices lies in exactly two cycles.
Circumference of a regular graph
Authors: Aung Min 
Published: June 2007

AbstractIt is proved that a 4‐connected, δ‐regular graph G either is Hamiltonian, or has at least 3δ + 1 vertices and contains a cycle of length at least min{4δ ‐ 4, 1/2 (|G| + 3δ ‐ 2)}. Examples supplied by B. Jackson and H.A. Jung show that min{4δ ‐ 4, 1/2(|G| + 3δ ‐ 2)} cannot be replaced by 4δ + 1.
Common root functions of two digraphs
Authors: Mao‐cheng Cai 
Published: June 2007

AbstractLet D1 and D2 be finite digraphs, both with vertex set V, let a and b be given functions from V to Z+, and let k be a positive integer. In this paper we give a necessary and sufficient condition for the existence of k arc‐disjoint arborescences in each of D1 and D2 satisfying the condition that for each v in Vmagnified image a(v) <r1(v) = r2(v) < b(v).Where ri(v) denotes the number of the arborescences in Di rooted at v, i = 1, 2.
Dynamic Stress Concentration around a Rectangular Crack in an Infinite Elastic Medium
Authors: Itou S. 
Published: June 2007

AbstractThe three‐dimensional problem of diffraction of elastic waves by a rectangular crack in an infinite elastic medium is investigated in this paper. The Fourier transform technique is used to reduce the problem to a solution of two simultaneous integral equations. To solve these equations, the crack surface displacement is expanded in a function with a double series. The unknown coefficients accompanied in that series are calculated with the aid of the Schmidt method. The dynamic stress intensity factors and the crack surface displacement are numerically computed.
Verallgemeinerte m‐Punkt‐Sekantenverfahren für schwach besetzte nichtlineare Gleichungssysteme
Authors: Mönch W. 
Published: June 2007

AbstractEs werden verallgemeinerte m‐Punkt‐Sekantenverfahren zur Lösung nichtlinearer Gleichungssysteme angepaßt an Aufgaben mit schwach besetzter Jacobi‐Matrix. Diese angepaßten Algorithmen werden an einigen numerischen Beispielen mit dem Verfahren von Schubert verglichen.
Optimization of Nordsieck's Method for the Numerical Integration of Ordinary Differential Equations
Authors: Gmelig R. H. J. , Traas C. R. 
Published: June 2007

AbstractStability and accuracy of Nordsieck's integration method can be improved by choosing the zero‐positions of the extraneous roots of the characteristic equation in a suitable way. Optimum zero‐positions have been found by minimizing the lower bound of the interval of absolute stability and the coefficient of the truncation error. Various properties of the improved methods have been analysed, such as the behaviour of the high‐order terms, the equivalence with multistep methods and the damping of perturbations.
Pressure Loaded Structures under Large Deformations
Authors: Bufler H. 
Published: June 2007

AbstractPressure loads are configuration dependent. The magnitude of the pressure may be considered as a function of the Eulerian or the Lagrangian coordinates respectively. The first (natural) case turns out to be conservative if a certain line integral vanishes; the second (artificial) one is always nonconservative. Basing on the theory of potential operators the condition for the conservativeness of a pressure loading acting on a finitely deformed structure is derived and the corresponding potential and incremental potential are calculated. They are needed for the variational principles of conservative elastic boundary value problems. In the nonconservative case the principle of virtual displacements and its incremental version respectively serve as an adequate description.
The Role of the Tangent Mapping in Analyzing Bifurcation Behaviour
Authors: Fink J. P. , Rheinboldt W. C. 
Published: June 2007

AbstractIn the study of solution manifolds of parameter‐dependent nonlinear equations extended systems of equations play an important role, especially for the computation of singular points, such as turning points, bifurcation points, etc. Various extended systems have been proposed in the literature. Here it is shown that a central feature in the construction of extended systems is the tangent map of differential geometry. A theory of extended equations based on the tangent map is presented which also exhibits the close connection with the choice of local coordinate systems. The ideas and results are illustrated with an example of a continuously stirred chemical reactor.
Zur Darstellung des turbulenten Wärmestroms
Authors: Oswatitsch K. 
Published: June 2007

AbstractDas Gesetz für den turbulenten Wärmestrom wird auf neuem Wege Über einen Entropieerhaltungssatz hergeleitet. Es besagt, daß der Wärmestrom proportional zum Gefälle der potentiellen Temperatur oder zum Entropiegefälle ist und nicht zum Gefälle der Temperatur, wie dies die Fouriersche Wärmeleitungsgleichung aussagt. Der Unterschied ist insbesondere für turbulente Grenzschichten der Atmosphäre von Bedeutung, weil dort die beiden Gefälle entgegengesetzt gerichtet sein können.
Über explizite, halbimplizite und implizite Algorithmen zur endlichen und iterativen Transformation von Matrizenpaaren
Authors: Falk S. 
Published: June 2007

AbstractMit Hilfe einer neuen Strategie werden einige der bekannten multiplikativen Algorithmen (HOUSEHOLDER, HESSENBERG, DANILEWSKI, JACOBI u. a.) auf reguläre Paare verallgemeinert, ohne daß die Matrix B−1A oder eine ihr gleichwertige Umformung explizit berechnet werden müßte.
On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
Authors: Oleinik O. A. , Shamaev A. S. , Yosifian G. A. 
Published: June 2007

AbstractIn this paper we study the convergence of energy integrals, stress tensors and frequencies of free vibrations for non‐homogeneous and porous elastic bodies with a periodic structure of period ε as ε → 0. The results are based on the estimates for solutions of the boundary value problem of the elasticity system with rapidly oscillating periodic coefficients, obtained in [4], [11].
Fehlerabschätzung für eine Differenzenmethode zur Approximation schwacher Lösungen von Stefan‐Aufgaben
Authors: Streit U. , Weinelt W. 
Published: June 2007

AbstractIn der Arbeit wird eine implizite Differenzenmethode (Gitterparameter h, τ) zur Berechnung der schwachen Lösung einer eindimensionalen Stefan‐Aufgabe betrachtet, wobei die Enthalpiefunktion geeignet approximiert wird (Parameter Δ). Unter Schwachen Regularitätsvoraussetzungen werden Fehlerabschätzungen für diese Methode gefunden. Hauptresultat ist eine Konvergenzordnung von O(Δ1/4 + h½ + τ½) in der L2‐Norm.
A Survey of One‐Step Splitting Methods for Semi‐Discrete First Order Hyperbolic Partial Differential Equations
Authors: de Vries H. B. 
Published: June 2007

AbstractIn this paper spliting methods are discussed for first order hyperbolic partial differential equations via the method of lines, and in particular the time integration will be discussed. A class of one‐step integration formulas is defined, which is shown to contain several well‐known spliting methods. For a number of methods stability results are given.
Die Onsagerschen Reziprozitätsbeziehungen in der Thermodynamik der Boltzmann‐Volterra‐Materialien
Authors: Mazilu P. 
Published: June 2007

AbstractDie bekannte Vermutung von Onsager, daß die thermomechanischen Symmetriebeziehungen eine Folge der Zeit‐Mikroreversibilität sind, wird für viskoelastische Boltzmann‐Volterra‐Materialien, die konstitutive Inertialsysteme bilden, bewiesen.
Tensor Functions Representations as Applied to Deriving Constitutive Relations for Skewed Anisotropy
Authors: Basista M. 
Published: June 2007

AbstractAn irreducible, non‐polynomial representation is established for an anisotropic constitutive equation being an explicit relation between two symmetric, second‐order tensors. The considered material anisotropy is characteristic of two non‐orthogonal and mechanically non‐equivalent privileged directions in plane. Particular cases of orthotropy and of cubic symmetry are analyzed in detail. An illustrative example referring to infinitesimal elasticity is presented in order to compare the developed representation with the classical Hooke law.
Bemerkungen zur numerischen Behandlung einer Klasse von schwach singulären Integralgleichungen 1. Art unter Verwendung von Kollokations‐ und Galerkin‐Methoden
Authors: El‐Seoud M. S. Abou 
Published: June 2007

AbstractEs werden die beiden folgenden Algorithmen zur numerischen Lösung einer Klasse von schwach singulären Integralgleichungen erster Art mit logarithmischem Kern sowohl bezüglich Konvergenzordnung also auch Rechenaufwand verglichen:

das Galerkinverfahren unter Verwendung finiter Elemente mit stückweise konstanten, linearen und quadratischen Ansatzfunktionen,
die Kollokationsmethode mit stückweise konstanten Ansatzfunktionen.
Beide Verfahren werden wir bei mehreren Stützstellenzahlen vergleichen. Solche Klassen von Integralgleichungen resultieren aus dem Dirichletproblem für stark elliptische Differentialgleichungen unter Verwendung der Fundamentallösung. Diese Klassen von Integralgleichungen sind mittels des Galerkinverfahrens in der letzten Zeit untersucht worden — siehe z. B. [7] und [8]. Die Kollokationsmethode zeichnet sich durch ihren einfachen Formalismus sowie durch ihren niedrigen Rechenaufwand aus und wird in der Praxis insbesondere von Ingenieuren viel verwendet. Eine Fehlerabschätzung für die Kollokationsmethode in der Maximum‐Norm wurde u. W. erstmals in [1] hergeleitet. Für Galerkin‐ Verfahren, angewandt auf Randintegralgleichungen für gemischte Randwertprobleme, wurden kürzlich sowohl theoretische als auch experimentielle asymptotische Fehlerabschätzungen in [9] und [10] hergeleitet. Für die Kollokationsmethode unter Benutzung von ungeraden Splinepolynomen erhält man im Falle einer ziemlich allgemeinen Klasse streng elliptischer Pseudodifferentialoperatoren in einer Unabhängigen ein erstes Konvergenzergebnis in verschiedenen Sobolevnormen für die entsprechenden Randintegralgleichungen [3].
Combined Residual Natural and Marangoni Convection in a Liquid Sphere Subjected to a Constant and Variable Micro‐Gravity Field
Authors: Bauer H. F. 
Published: June 2007

AbstractThe combined effect of thermal Marangoni convection induced by a gradient of temperature imposed upon the free surface of a liquid sphere and the residual natural convection steming from the still existing micro‐gravity field in an orbiting space laboratory has been investigated. The case of a constant and linearly dependent axial residual gravity field has been considered, for which the Stokes equation in the approximation of Boussinesq have been solved. By the introduction of a dynamic Bond‐number derived as the ratio of the Grashof number to the Reynoldsnumber based upon the Marangoni flow the predominance of Marangoni‐ (for B̃o → 0) or natural convection (for B̃o → ∞) could be determined. Streamlines, radial‐ and angular velocity distributions have been obtained analytically. The combined effect of Marangoni‐ and natural convection is of importance for space processings. In addition the isothermal lines are presented for various imposed temperature distributions at the free surface of the liquid sphere.
Quasigeneralisierte Variable
Authors: Baumgarte J. , Ostermeyer G. P. 
Published: June 2007

AbstractThe numerical solution of a system of differential and algebraic equations is difficult, because there can appear numerical instabilities with respect to the algebraic equations. This paper deals with a method, which allows to get numerical solutions of the system, satisfying the algebraic constraint equations exactly without reduction of the order of the differential equations. The method is demonstrated by examples from mechanics.
Über Variablentransformationen an klassischen Bewegungsgleichungen
Authors: Gerlich G. 
Published: June 2007

AbstractFür die Transformation der abhängigen und unabhängigen Veränderlichen bei klassischen Bewegungsgleichungen werden allgemeine, explizite Formeln für die Geschwindigkeits‐ und Beschleunigungsfelder abgeleitet. Diese Formeln liefern ein Kriterium für kanonische Transformationen und werden u. a. mit dem Beispiel der Lorentztransformationen erläutert. Dies führt zu einer rein mathematischen Ableitung des sogenannten Additionstheorems relativistischer Geschwindigkeiten. Die transformierten elektromagnetischen Felder ergeben sich aus der Bewegungsgleichung des Punktelektrons, ohne die Form der Maxwellschen Gleichungen zu verwenden.
Two Waveguide Bifurcation Problems
Authors: Lüneburg E. , Hurd R. A. 
Published: June 2007

AbstractWe condsider the diffraction of the dominant wave mode in a parallel plate waveguide with hard and soft boundaries incident on a centred half plane on whose two faces hard and soft boundary conditions obtain. A closed form solution of the resulting coupled Wiener‐Hopf system is derived. The modal amplitudes in all three regions are calculated and the relative powers of the low order modes versus the plate spacing are displayed graphically.
Über einen numerischen Zugang zur Lösungs‐ und Eigenwerttheorie von elliptischen Systemen partieller Differentialgleichungen
Authors: Beckert H. 
Published: June 2007

AbstractDie Approximation von Greenschen Tensoren zu selbstadjungierten Randwertproblemen stark elliptischer Systeme 2m‐ter Ordnung über G ⊂ Rn wird durch die Minimalwerte von Variationsproblemen von oben und mit Hilfe der Dualitätstheorie durch Maximalwerte von unten abgeschätzt. Im wichtigen Fall 2m ≦ n erhalten wir starke Konvergenzaussagen durch Regularisierung und Anwendung der Schauderschen Abschätzungen. Für die zugehörigen Eigenwertprobleme ergeben sich weiter neue Abschätzungen in der Approximationstheorie von Eigenwerten.
Weiteres über Pseudo‐Divisionsverfahren zur Berechung der Standardfunktionen und gewisser Nicht‐Standardfunktionen
Authors: Bittner L. 
Published: June 2007

AbstractEs werden einige Gesichtspunkte, welche nach Meinung des Verfassers die theoretische Grundlage der sogenannten Pseudo‐Divisionsverfahren (CORDIC) bilden, dargelegt. Es wird eine aditive und multiplikative Darstellung von reellen Argumenten durch Basisargumente angegeben und gezeigt, wie die unausgesprochenen Ideen der Pseudodivisionsverfahren dazu aus genutzt werden können, um neue Algorithmen für gewisse Funktionen, welche eine Art Additions‐ oder Multiplikationstheorem erfüllen, und für ihre Inversen herzuleiten.
Fluidelastische Schwingungen
Authors: Mahrenholtz O. 
Published: June 2007

AbstractFluidelastische Schwingungen entstehen aus dem Zusammenwirken von Strömung und Strukturbewegung. Während man das Verhalten schwingender Strukturen gut berechnen kann, trifft dies für das interaktive (Um‐) Strömungsfeld nur bedingt zu. Daher arbeitet man mit Modellen, die an dominanten Phänomenen orientiert sind. Es wird über die wesentlichen Modelle, nämlich Flattern, Formanregung und Wirbelanregung, berichtet. Zur Wirbelanregung werden neuere Erkenntnisse mitgeteilt.