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Long cycles in bipartite tournaments

✍ Scribed by Jianzhong Wang

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 318 KB
Volume: 148
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00273-l

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✦ Synopsis

A digraph D is said to satisfy the condition O(n) ifd~-(u) + d r (v) >t n whenever uv is not an arc of D. In this paper we prove the following results: If a p x q bipartite tournament T is strong and satisfies O(n), then T contains a cycle of length at least min(2n + 2, 2p, 2q}, unless T is isomorphic to a specified family of graphs. As an immediate consequence of this result we conclude that each arc of a n x n bipartite tournament satisfying O(n) is contained in cycles of lengths 4, 6 ..... 2n, except in a described case.

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