A Complete Solution of a Problem of Bondy Concerning Multipartite Tournaments

Ann-partite tournament is an orientation of a completen-partite graph. In 1976, Bondy raised the following problem: does every strongn-partite (n⩾5) tournament, in which each partite set has at least two vertices, contain an (n+1)-cycle? It is the purpose of this paper to give a characterization of all suchn-partite tournaments without (n+1)-cycle.