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Cycles through a given set of vertices in regular multipartite tournaments

Stefan Winzen|Lutz Volkmann
대한수학회 (The Korean Mathematical Society)|2007.05|대한수학회지 (Journal of the KMS)|제44권 제3호|pp. 683-695

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Abstract

A tournament is an orientation of a complete graph, and in generala multipartite or c-partite tournament is an orientation of acomplete c-partite graph.In a recent article, the authors proved that a regular c-partitetournament with r ge 2 vertices in each partite set contains acycle with exactly r-1 vertices from each partite set, withexception of the case that c = 4 and r = 2. Here we willexamine the existence of cycles with r-2 vertices from eachpartite set in regular multipartite tournaments where the r-2vertices are chosen arbitrarily. Let D be a regular c-partitetournament and let X subseteq V(D) be an arbitrary set withexactly 2 vertices of each partite set. For all c ge 4 wewill determine the minimal value g(c) such that D-X isHamiltonian for every regular multipartite tournament with r geg(c).

참고문헌 (18)

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