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Paper   IPM / M / 105
School of Mathematics
  Title:   On uniquely list colorable graphs
1.  M. Ghebleh
2.  E. S. Mahmoodian
  Status:   Published
  Journal: Ars Combin.
  Vol.:  59
  Year:  2001
  Pages:   307-318
  Supported by:  IPM
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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