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Cycles Containing a Given Arc in Regular Multipartite Tournaments

โœ Scribed by Guo-fei Zhou; Ke-min Zhang


Publisher
Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2002
Tongue
English
Weight
104 KB
Volume
18
Category
Article
ISSN
0168-9673

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๐Ÿ“œ SIMILAR VOLUMES


A remark on cycles through an arc in str
โœ Lutz Volkmann ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 140 KB

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 โ‰ฅ 3 contains an arc that belongs to a directed cycle of length m for every m โˆˆ {3, 4, . . . , c}.

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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 โ‰ฅ 3 contains three arcs that belong to a cycle of length m for each m โˆˆ {3, 4,

Complementary cycles containing a fixed
โœ Ke Min Zhang; Yannis Manoussakis; Zeng Min Song ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 250 KB

Let (x, y) be a specified arc in a k-regular bipartite tournament B. We prove that there exists a cycle C of length four through (x, y) in B such that B-C is hamiltonian.