Showing papers in "Journal of Combinatorial Theory, Series B in 2001"

TL;DR: Let c(t) be the minimum number c such that every graph G with e(G)?c|G| contracts to a complete graph Kt where ?=0.319... is an explicit constant.

TL;DR: It is proved that every directed graph with no “haven” of large order has small tree-width, and the Hamilton cycle problem and other NP-hard problems can be solved in polynomial time when restricted to digraphs of bounded tree- width.

TL;DR: It is established necessary and sufficient conditions for decomposing the complete graph of even order minus a 1-factor into even cycles and the completegraph of odd order into odd cycles.

TL;DR: The maximum degree seven case is proved, which proves that planar graphs of maximum degree at least eight have the edge chromatic number equal to their maximum degree.

TL;DR: The following sharp upper bound is obtained of the minimum degree of vertices of G, which is either a regular graph or a bidegreed graph in which each vertex is of degree either ? or n?1.

TL;DR: The complete lists were determined with the help of a parallel program which finds all normal subgroups of low index in a finitely-presented group.

TL;DR: The spectral radius of graphs with n vertices and k cut vertices is studied and the graph that has the maximal spectral radius in this class is described.

TL;DR: In this article, it was shown that a set W 0 of vertices is a dynamic monopoly or dynamo if starting the game with the vertices of W 0 colored white, the entire system is white after a finite number of rounds.

TL;DR: The main result is the linear lower bound g ( G )⩾ τ /160 (if G − w is 3-connected and τ >1) and it is proved that the minimum face cover problem is NP -hard for planar triangulations and the minimum vertex cover is NP-hard for 2-connected cubic planar graphs.

TL;DR: It is shown how the result with four matchings implies that a random d-regular graph for fixed even d?4 asymptotically almost surely decomposes into d/2 Hamilton cycles.

TL;DR: It is shown that it suffices to prove the 3-flow conjecture of Tutte that every bridgeless graph without a 3-edge cut has a nowhere-zero 3- flow for 5-edge-connected graphs.

TL;DR: It is shown that, for any odd prime p, integers n?3 and k?2 such that k divides p?1, there are exactly (pn?2?1)/2+pn?3?1 nonisomorphic connected half-transitive metacirculants of order pn and valency 2k.

TL;DR: A proof of this conjecture is given in this paper that a signed graph is weakly bipartite if and only if it does not contain a minor called an odd K5.

TL;DR: It is shown that two orientable embeddings of Kn+1 generated by schemes are isomorphic if and only if (?1, ?2, ?, ?n) is an automorphism of ?.

TL;DR: The random graphs G(n, Pr(edge)=p), G( n, #edges=M) at the critical range p=(1+?n?1/3)/n and M=(n/2)(1+)?n? 1/3) are studied and the limiting distribution of the largest component size is determined.

TL;DR: The Steinitz representations of 3-connected planar graphs correspond, in a well described way, to Colin de Verdi?re matrices of such graphs, to prove a conjecture of Connelly on the eigenvalues of stress matrix of braced convex polytopes.

TL;DR: A new upper bound of ?

TL;DR: A short proof of Mader's min-max theorem for the maximum number of disjoint S-paths is given.

TL;DR: This work describes the simple T-modules, a 2-homogeneous bipartite distance-regular graph with diameter D?3 and valency k?3, and gives three sets of generators for T, two of which satisfy the relations of the quantum universal enveloping algebra of the Lie algebra sl(2).

TL;DR: It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s?3 and that an SOTA graph is a normal cover of a graph for which there is an automorphism group that is almost simple and s- transitive.

TL;DR: It is proved that the roots of the chromatic polynomial of a k-ary generalized theta graph all lie in the disc|z?1|?1+o(1)]k/logk, uniformly in the path lengths si, and it is conjecture that this holds for all k.

TL;DR: The purpose of this paper is to show that every k-connected tournament with at least 8k vertices contains k vertex-disjoint directed cycles spanning the vertex set.

TL;DR: The main upper bound is proved by establishing an upper bound on the number of vertices which must be removed from a graph of bounded degree in order to leave a planar graph.

TL;DR: Complete sets of eigenfunctions are obtained for several related families, and the results are used to provide information about the location of the zeros of the associated chromatic polynomials.

TL;DR: It is shown that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2r+1, and that this bound is tight.

TL;DR: It is shown that any H-minor free graph G of high enough girth has circular chromatic number arbitrarily close to two, and each such graph G admits a homomorphism to a large odd circuit.

TL;DR: A family of the currently largest known vertex-transitive graphs of degree d, diameter 2, and order 89(d+12)2, for infinitely many values of d is constructed.

TL;DR: A conjecture of Brylawski, namely that the Tutte polynomial of a connected matroid is irreducible over the integers, is solved.

TL;DR: It is proved that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph.

TL;DR: It is proved that a noncomplete ?-connected graph for which the sum of the degrees of any two distinct vertices is at least 2?54???1 possesses a ?-contractible edge.