Three supplements to Reid's theorem in multipartite tournaments
Discrete Applied Mathematics
Complementary cycles in almost regular multipartite tournaments, where one cycle has length four
Discrete Applied Mathematics
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An n-partite tournament is an orientation of a complete n-partite graph. If D is a strongly connected n-partite (n≥3) tournament, then we shall prove that every partite set of D has at least one vertex which lies on a cycle Cm of each length m for * such that V(C3)⊂V(C4)⊂⋯⊂V(Cn), where V(Cm) is the vertex set of Cm for *. This result extends those of Bondy [2], Guo and Volkmann [4], Gutin [6], Moon [8], and Yeo [12].