Journal•ISSN: 0095-8956
Journal of Combinatorial Theory, Series B
Elsevier BV
About: Journal of Combinatorial Theory, Series B is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Chordal graph & Matroid. It has an ISSN identifier of 0095-8956. Over the lifetime, 3240 publications have been published receiving 117227 citations.
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TL;DR: An algorithm, which for fixed k ≥ 0 has running time O (| V(G) | 3 ), to solve the following problem: given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs.
1,438 citations
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.
912 citations
TL;DR: Wagner's conjecture is proved, that for every infinite set of finite graphs, one of its members is isomorphic to a minor of another.
898 citations
TL;DR: It is shown that if a sequence of dense graphs G has the property that for every fixed graph F, the density of copies of F in G"n tends to a limit, then there is a natural ''limit object,'' namely a symmetric measurable function W:[0,1]^2->[0, 1].
882 citations
TL;DR: It is proved that for every planar graph H there is a number w such that every graph with no minor isomorphic to H can be constructed from graphs with at most w vertices, by piecing them together in a tree structure.
818 citations