正则多部竞赛图中的分量共轭圈

Componentwise Complementary Cycles in Diregular Multipartite Tournaments

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。论文根据分量共轭圈(componentwisecomplementarycycles)的定义,证明了:如果D是一个正则的n-部竞赛图(n≥4),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。

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.lf 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 T7^1 .This result gives impetus to resolving Yeo＇s conjecture and the problem of complementary cycles in multipartite digraph.