强多部竞赛图中的过两条弧的圈
On cycles through two arcs in strong multipartite tournaments
摘要：
多部竞赛图是完全$c$ -部图的一个定向图.在[L.李文，强连通多部竞赛图中弧上圈的一个注记，应用数学通讯。20（2007）1148--1150]中，Reynmann证明了具有$c \ge 3$的强连通$c$ -部竞赛图对于每个$m \in \{3, 4, \ldots, c\}$都包含属于长度为$m$的有向圈的弧。他还证明了三个弧的存在与此属性。本文证明了两条这样的弧的存在性。
英文摘要：
A multipartite tournament is an orientation of a complete $c$-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148--1150], Volkmann proved that a strongly connected $c$-partite tournament with $c \ge 3$ contains an arc that belongs to a directed cycle of length $m$ for every $m \in \{3, 4, \ldots, c\}$. He also conjectured the existence of three arcs with this property. In this note, we prove the existence of two such arcs.
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