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Tournament pathwidth and topological containment

Author(s): Fradkin, Alexandra; Seymour, Paul D.

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Abstract: We prove that if a tournament has pathwidth >= 4 theta(2) + 7 theta then it has theta vertices that are pairwise theta-connected. As a consequence of this and previous results, we obtain that for every set S of tournaments the following are equivalent: there exists k such that every member of S has pathwidth at most k, there is a digraph H such that no subdivision of H is a subdigraph of any member of S, there exists k such that for each T is an element of S, there do not exist k vertices of T that are pairwise k-connected. As a further consequence, we obtain a polynomial-time algorithm to test whether a tournament contains a subdivision of a fixed digraph H as a subdigraph. (C) 2013 Elsevier Inc. All rights reserved.
Publication Date: May-2013
Electronic Publication Date: 26-Mar-2013
Citation: Fradkin, Alexandra, Seymour, Paul. (2013). Tournament pathwidth and topological containment. JOURNAL OF COMBINATORIAL THEORY SERIES B, 103 (374 - 384. doi:10.1016/j.jctb.2013.03.001
DOI: doi:10.1016/j.jctb.2013.03.001
ISSN: 0095-8956
Pages: 374 - 384
Type of Material: Journal Article
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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