Showing papers in "Journal of Combinatorial Theory, Series B in 1985"

TL;DR: This method uses the second smallest eigenvalue of a certain matrix associated with the graph and it is the discrete version of a method used before for Riemannian manifolds for asymptotic isoperimetric inequalities for families of graphs.

TL;DR: A class of graphs is introduced which includes both triangulated graphs and complements of triangulate graphs, and a structural theorem leads to a proof that weakly triangulation graphs are perfect.

TL;DR: This work first establishes a certain property of minimal imperfect graphs and then uses it to generate large classes of perfect graphs, which are then used to establish and generate large numbers of minimal perfect graphs.

TL;DR: It is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time, and it is shown that the strong perfect graph conjecture holds for EPT graphs.

TL;DR: This paper classifies the regular imbeddings of the complete graphs Kn in orientable surfaces and shows that these maps are all equivalent under Wilson's map-operations Hi, and determined for which n they are reflexible or self-dual.

TL;DR: This result is extended, showing that if G is a graph with a given genus k, then 3 + 2k pursuers are enough to “arrest” the evader B.

TL;DR: The problem of colouring the real line so that the distance between like coloured numbers does not lie in some specified set D, called the distance set, is discussed.

TL;DR: The integral multicommodity flow problem is proved to belong to the problem class P when the underlying graph is outerplanar and the proof gives rise to an algorithm of complexity O( |V|3log|V|).

TL;DR: It is shown that nonplanar graphs G with κ ( G )≥4, such that G -{ e } for some edge e is planar, are (3,2)-pendant tree-connected.

TL;DR: Finite permutation groups of rank 3 such that both the subconstituents have rank 3 are classified because every isomorphism between subgraphs on at most three vertices is a restriction of an automorphism of the graph.

TL;DR: A method is given for solving extremal problems of the following type: determine the maximal number of vertices in a class of hypergraphs, and results are applied for τ-critical and ν-criticalhypergraphs.

TL;DR: It is shown that 3-connected cubic bipartite planar graphs with fewer than 66 vertices are Hamiltonian.

TL;DR: Here the following conjecture of Fink and Jacobson is proved: for any simple graph G and any positive integer k, γ k (G ) ≤ β k ( G ).

TL;DR: X can be uniquely reconstructed from the unlabeled graphs X1 and Xn, and the proof uses linear algebra and does not explicitly describe the reconstructed graph X.

TL;DR: If G is a k-connected graph, such that the degree-sum of any k + 1 independent vertices is at least m, then G contains a cycle of length at least: Min(2m(k + 1), n) (n denotes the order of G).

TL;DR: A new notion of connection in graphs is introduced, called n -biconnection, and an analogous theorem for graphs and their bicircular matroids is proved.

TL;DR: Subgraphs induced by vertex neighbourhoods in distance-regular graphs where cycles do not exist are related to certain strongly regular graphs.

TL;DR: It is proved that a DR graph H without triangles can be obtained as a component of G (2) if and only if it is a (k, g) -graph with g ≥ 4.

TL;DR: This poster presents a probabilistic reconstruction of the response of the immune system to the presence of polypeptide-like substances, which secrete polymethine, a substance which is believed to be a component of DNA.

TL;DR: It is shown that a 1-factorization exists for all generating sets for even order abelian groups, dihedral groups, and dicyclic groups and for all minimal generating setsFor even order nilpotent groups andFor Dm × Zn.

TL;DR: This work proves constructively duality theorems of linear and quadratic programming in the combinatorial setting of oriented matroids and suggests the study of properties of square matrices such as symmetry and positive semi-definiteness in the context of orientedMatroids.

TL;DR: La nature geometrique de the decomposition utilisee pour etablir cette relation fonctionnelle conduit a definir une notion naturelle de carte interieure a une carte planaire pointee.

TL;DR: The symmetric genus of a finite group G has been defined by Thomas W. Tucker as the smallest genus of all surfaces on which G acts faithfully as a group of automorphisms (some of which may reverse the orientation of the surface).

TL;DR: It is proved that D 0 corresponds to a forest, which implies that in a finite, minimally n -connected digraph D , the number of vertices of outdegree n is at least n and that the numberof vertices with outdegree or indegree equal to n grows linearly in | D |.

TL;DR: This result is used to determine the minimum number of edges required in a bipartite graph to ensure a cycle of length at least 2 m, for any integer m ≥ 2.

TL;DR: A strengthened version of this theorem for binary matroids says that to any binary matroid at least one of the following statements must apply: (1) the matroid is decomposable, (2) several elements can be removed (in any order) without destroying 3-connectivity.

TL;DR: It is shown that the independent set numbers of polygon matroids of outerplanar graphs are log concave.

TL;DR: The paper is concerned with the longest cycles in regular three- (or two-) connected graphs and proves that every 3-connected k-regular graph on n vertices has a cycle of length at least min(3k, n).

TL;DR: It is proved that any bridgeless graph G, G = (V, E), |E| = m, |V| = N, admits a cycle cover of total length at most m + 54(n − 1).

TL;DR: In this article, it was shown that a graph is perfect if its vertices can be coloured by two colours in such a way that each induced chordless path with four vertices has an odd number of vertices of each colour.