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On cycles through a given vertex in multipartite tournaments

✍ Scribed by Yubao Guo; Axel Pinkernell; Lutz Volkmann

Book ID: 108316050
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 283 KB
Volume: 164
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00048-9

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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}.