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 t...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 componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite （n 〉 6） tournament that is not a tournament. Let C be a 3-cycle of D and D ／ V（C） be nonstrong. For the unique acyclic sequence D1, D2,..., Da of D ／ V（C）, where a 〉 2, let Dc = {Di｜Di contains cycles, i = 1,2,...,a}, Dc = {D1,D2,...,Da} ／ De. If Dc≠ 0, then D contains a pair of componentwise complementary cycles.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10801114)the Nature Science Foundation of Shandong Province, China (No. ZR2011AL019 No. ZR2011AM005)
文摘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 componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite （n 〉 6） tournament that is not a tournament. Let C be a 3-cycle of D and D ／ V（C） be nonstrong. For the unique acyclic sequence D1, D2,..., Da of D ／ V（C）, where a 〉 2, let Dc = {Di｜Di contains cycles, i = 1,2,...,a}, Dc = {D1,D2,...,Da} ／ De. If Dc≠ 0, then D contains a pair of componentwise complementary cycles.
