When n-cycles in n-partite tournaments are longest cycles
نویسندگان
چکیده
An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.
منابع مشابه
Multipartite tournaments with small number of cycles
L. Volkmann, Discrete Math. 245 (2002) 19-53 posed the following question. Let 4 ≤ m ≤ n. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n − m + 1 cycles of length m? We answer this question in affirmative. We raise the following problem. Given m ∈ {3, 4, . . . , n}, find a characterization of strong n-partite tournaments having exactly n −m + 1 cycle...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 289 شماره
صفحات -
تاریخ انتشار 2004