“School of Mathematics”
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Paper IPM / M / 105  


Abstract:  
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 klist colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2list
colorable graphs. Here we state some results which will pave the way in characterization of uniquely klist 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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