Paths with a given number of vertices from each partite set in regular multipartite tournaments Original Research Article

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. For image we prove that a regular c-partite tournament with image vertices in each partite set contains a directed path with exactly two vertices from each partite set. Furthermore, if image, then we will show that almost all regular c-partite tournaments D contain a directed path with exactly image vertices from each partite set for each given integer image, if r is the cardinality of each partite set of D. Some related results are also presented.