正则竞赛图的有向生成三角形

Spanning Directed Triangles in Regular Tournaments

2008年N.Lichiardopol在离散数学-竞赛图中经过给定0,1,2个公共顶点的圈.一文中提出以下公开问题:阶为2n+1的正则竞赛图T,对于任意的x∈V(T)是否存在n个有向三角形Ti使得V(Ti)∩V(Tj)=x(1≤i≤j≤n).文章证明了对于阶数为5,7,9的正则竞赛图,该问题答案是肯定的.

In 2008,N.Lichiardopol raised the open problem in his article-Cycles in a tournament with pairwise zero,one or two given vertices in common Discrete Math：for regular tournaments T of order 2n＋1,is that true for any vertex x∈V（T） that there exists n triangles Ti and V（Ti）∩V（Tj）=x for 1≤ij≤n.In this paper,we proved that the problem is right,where regular tournaments with vertices of 5,7,9.