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|Paper IPM / M / 105||
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 k-list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2-list
colorable graphs. Here we state some results which will pave the way in characterization of uniquely k-list colorable graphs. There is a relationship between this concept and defining sets in graph colorings and critical sets in latin squares.
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