The partition of a strong tournament Original Research Article

A digraph T is strong if for every pair of vertices u and image there exists a directed path from u to image and a directed path from image to u. Denote the in-degree and out-degree of a vertex image of T by image and image, respectively. We define image and image. Let image be a 7-tournament which contains no transitive 4-subtournament. In this paper, we obtain some conditions on a strong tournament which cannot be partitioned into two cycles. We show that a strong tournament T with image vertices such that image and image can be partitioned into two cycles. Finally, we give a sufficient condition for a tournament to be partitioned into k cycles.