Weakly complementary cycles in a class of multipartite tournaments

The problem of complementary cycles in tourname-nts and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n -partite digraphs with n ≥3 is still open. Based on the definition of weakly complementary cycles, we get the following result. Let D be a 2 -strong n -partite tournament that is not a tournament, where n ≥6 . Let C be a 3 -cycle of D and D−V(C) be nonstrong. For the unique acyclic sequence D1,D2,…, Dα of D−V(C), where α≥2 , if 1 |V(Dα+1−i)|= 1, Di contains cycles for i = 1 or i = α, then D contains a pair of weakly complementary cycles.