中文摘要：

Guo（Discrete Appl.Math.95（1999）273-277）提出外路的概念.有向图中一个顶点x（或弧xy）的一条外路是指起始于x（或弧xy）的一条路使得x控制这条路的终点仅当终点也控制x.一条长为k的外路称为k-外路.本文证明了一个几乎正则c-部（c≥8）竞赛图D中,如果D的每个部集至少包含两个点,则D中每条弧有（k-1）-或k-外路,其中k∈{3,4,…,｜V（D）｜-1}.进一步,当D是一个几乎正则c-部（c≥8）竞赛图,且每个部集所含顶点数目相同时,D的每条弧在k-或（k＋1）-圈中,其中k∈{3,4,…,｜V（D）｜-1}.

英文摘要：

Guo （Discrete Appl. Math. 95 （1999） 273-277） proposed the concept of out-path. An outpath of a vertex x （an arc xy, respectively） in a digraph is a path starting at x （an arc xy, respectively） such that x dominates the endvertex of the path only if the endvertex also dominates x. A k-outpath is an outpath of length k. In this article, the following results are proved： Let D be an almost regular c-partite tournament. If each partite set contains at least two vertices, then every arc of D has a （k - 1）- or k-outpath for each k ∈ {3, 4,…, ｜V（D）｜- 1}. Furthermore, if D is an almost regular c-partite （c 〉 8） tournament with the partite sets V1, V2,…, Vc such that ｜V 1｜ = ｜V2｜ ｜Vc｜, then every arc of D is contained in a k- or （k ＋ 1）-cycle for each k ∈ {3,4,..., ｜V（D）｜ - 1}.