Graphs K_(1*4,5,) K_(1*5,4,), K_(1*4,4,) K_(2,3,4) have the property M(3)

摘要

Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely /c-list colorable graph. We say that a graph G has the property M(k) if and only if it is not uniquely fc-list colorable. M. Ghebleh and E. S. Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for the graphs K_(1*4,5,),K_(1*5,4,) K_(1*4,4,),K_(2,3,4,) and K_(2,2,r,) 4≤r≤8. In this paper we prove that the graphs K_(1*4,5,)_(1*5,4,) K_(1*4,4,) and K_(2,3,4,) have the property M(3).