On cycles through two arcs in strong multipartite tournaments
نویسنده
چکیده
A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148–1150], Volkmann proved that a strongly connected cpartite tournament with c > 3 contains an arc that belongs to a directed cycle of length m for every m ∈ {3, 4, . . . , c}. He also conjectured the existence of three arcs with this property. In this note, we prove the existence of two such arcs.
منابع مشابه
Cycles through a given arc and certain partite sets in strong multipartite tournaments
Moon [J. Combin. Inform. System Sci. 19 (1994), 207–214] showed that every strong tournament contains a Hamiltonian cycle through at least three pancyclic arcs. In this paper, we extend the result of Moon and prove that if D is a strong c-partite tournament with c ≥ 3, then D contains a cycle C containing vertices from exactly c partite sets such that C contains at least three arcs, each of whi...
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عنوان ژورنال:
- CoRR
دوره abs/1006.0902 شماره
صفحات -
تاریخ انتشار 2010