正则竞赛图的有向生成三角形  

Spanning Directed Triangles in Regular Tournaments

作　　者：李杰[1] 李世慧[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《太原师范学院学报（自然科学版）》2010年第3期21-23,共3页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：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.

关 键 词：互竞赛图 正则竞赛图 有向生成三解形集 

分 类 号：O157.5[理学—数学]