Weakly Complementary Cycles in a Class of Multipartite Tournaments

摘要

The problem of complementary cycles in tournaments 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 D_1, D_2,..., D_α of D - V(C), where α ≥ 2, if |V(D_(α+1-i)|= 1, D_i contains cycles for i=1 or i = α, then D contains a pair of weakly complementary cycles.