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

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 c⩾2c⩾2 we prove that a regular c  -partite tournament with r⩾2r⩾2 vertices in each partite set contains a directed path with exactly two vertices from each partite set. Furthermore, if c⩾4c⩾4, then we will show that almost all regular c-partite tournaments D   contain a directed path with exactly r-sr-s vertices from each partite set for each given integer s∈Ns∈N, if r is the cardinality of each partite set of D. Some related results are also presented.