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A remark on cycles through an arc in strongly connected multipartite tournaments

✍ Scribed by Lutz Volkmann

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 140 KB
Volume: 20
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2006.09.014

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✦ Synopsis

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}.

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Cycles through arcs in multipartite tournaments and a conjecture of Volkmann

✍ Hongwei Li; Shengjia Li; Yubao Guo; Qiaoping Guo 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 213 KB

Volkmann [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007Lett. 20 ( ) 1148Lett. 20 ( -1150] ] conjectured that a strong c-partite tournament with c ≥ 3 contains three arcs that belong to a cycle of length m for each m ∈ {3, 4,

Solution of a conjecture of Volkmann on

Solution of a conjecture of Volkmann on longest paths through an arc in strongly connected in-tournaments

✍ Dirk Meierling 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 139 KB 👁 1 views

## Abstract An in‐tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. Let __m__ = 4 or __m__ = 5 and let __D__ be a strongly connected in‐tournament of order ${{n}}\geq {{2}}{{m}}-{{2}}$ such that each arc belongs to a directed path of order at