正则多部竞赛图中的分量共轭圈

竞赛图的共轭圈问题已经完全解决, 而关于多部有向图的共轭圈问题仍然是一个open问题。 Yeo于1999年提出正则多部竞赛图包含共轭圈的猜想。本文根据分量共轭圈(componentwise complementary cycles)的定义, 证明了：如果D是一个正则的n-部竞赛图 ( )，则D包含一对分量共轭圈C1和C2，除非它同构于T71。 这对于解决Yeo的猜想和多部有向图的共轭圈问题有一定的意义。

Componentwise Complementary Cycles in Diregular Multipartite Tournaments

The problem of complementary cycles in tournaments has been completely solved.However,for semicomplete multi-partite digraphs,the problem of complementary cycles is still open.In 1999,Yeo presented conjecture which a diregular multipartite tournament has a pair of complementary cycles.In this paper,based on the definition of componentwise complementary cycles,we have gotten the following result.If D is a diregular n-partite(n≥4) tournament,then it contains a pair of componentwise complementary cycles C1 and C2,unless it is isomorphic to T17.This result gives impetus to resolving Yeo's conjecture and the problem of complementary cycles in multipartite digraph.