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
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
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.
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.
