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Notes on cycles through a vertex or an arc in regular 3-partite tournaments

✍ Scribed by Gaokui Xu; Shengjia Li; Qiaoping Guo; Hongwei Li

Book ID: 113449329
Publisher: Elsevier Science
Year: 2012
Tongue: English
Weight: 184 KB
Volume: 25
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.09.075

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A multipartite or c-partite tournament is an orientation of a complete c-partite graph. In this note we prove that a strongly connected c-partite tournament with c ≥ 3 contains an arc that belongs to a directed cycle of length m for every m ∈ {3, 4, . . . , c}.