Cycles in multipartite tournaments: results and problems Review Article

A tournament is an orientation of a complete graph, and in general a multipartite tournament is an orientation of a complete n-partite graph. Many results about cycles in tournaments are known, but closely related problems involving cycles in multipartite tournaments have received little attention until recently. We describe some of the rapid progress in recent years on this topic, including powerful new methods and techniques. This study give rise to various interesting problems and conjectures.