完全三部图K_(2,2,r),r=4,5,6,7,不是U3LC图

The complete tripartite graph K_(2,2,r),r=4,5,6,7, are not U3LC graph

M.Ghebleh和E.S.Mahmoodian在其开放问题中提出了完全三部图K2,2,r,r=4,5,6,7,是U3LC图还是具有M(3)性质这样一个问题。在这篇文章中我们叙述并证明了图K2,2,7具有M(3)性质这样一个主定理,进一步证明了图K2,2,r,r=4,5,6,也具有M(3)性质。

The problem that whether the complete tripartite graphs K2,2,r, for r = 4,5,6,7, are U3LC graph or have the property M（3） was put forward originally by M. Ghebleh and E. S. Mahmoodian. In this paper,that the graph K2,2,7 has the property M（3） is proved and, therefore,that the complete tripartite graphs K2,2,r.for r = 4,5,6,have the property M（3）.