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
In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, general...In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, generalizes a theorem due to Alspach.展开更多
A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path. This concept is a generalization of a directed...A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path. This concept is a generalization of a directed cycle. We show that if T is an almost regular n-partite (n>8) tournament with each partite set having at least two vertices, then every are of T has a k-outpath for all k, 3＜k＜n-1.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.
基金supported by Chinese Postdoctoral Science FoundationNational Natural Science Foundation of China(Grant Nos.60103021,10171062 and 19871040)Huazhong University of Science and Technology Foundation
文摘In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, generalizes a theorem due to Alspach.
基金the National Natural Science Foundation of China and NSFJC.
文摘A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path. This concept is a generalization of a directed cycle. We show that if T is an almost regular n-partite (n>8) tournament with each partite set having at least two vertices, then every are of T has a k-outpath for all k, 3＜k＜n-1.
