Abstract: The problem of complementary cycles in tournaments was 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 get the following result. If D is a diregular n-partite ( ) tournament, then it contains a pair of componentwise complementary cycles C1 and C2, unless it is isomorphic to T71. This result gives impetus to resolving Yeo's conjecture and the problem of complementary cycles in multipartite digraph.

摘要： 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。