An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c...An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c-partite digraph (c ≥ 3), and one of the partitesets of it consists of a single vertex, say v, then D has a c-pancyclic partial ordering from v,which generalizes a result about pancyclicity of multipartite tournaments obtained by Gutin in 1993.Then we prove that letting D be a strongly connected semicomplete c-partite digraph with c ≥ 3 andletting v be a vertex of D, then D has a (c - 1)-pan-outpath partly ordering from v. This resultimproves a theorem about outpaths in semicomplete multipartite digraphs obtained by Guo in 1999.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
文摘An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c-partite digraph (c ≥ 3), and one of the partitesets of it consists of a single vertex, say v, then D has a c-pancyclic partial ordering from v,which generalizes a result about pancyclicity of multipartite tournaments obtained by Gutin in 1993.Then we prove that letting D be a strongly connected semicomplete c-partite digraph with c ≥ 3 andletting v be a vertex of D, then D has a (c - 1)-pan-outpath partly ordering from v. This resultimproves a theorem about outpaths in semicomplete multipartite digraphs obtained by Guo in 1999.
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.
