A Characterization of Uniquely 2-List Colorable Graphs

  title={A Characterization of Uniquely 2-List Colorable Graphs},
  author={Mohammad Mahdian and Ebadollah S. Mahmoodian},
  journal={Ars Comb.},
Let G be a graph with vertices, and let S 1 ; S 2 ; : : : ; S be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely k{list colorable graph. We prove that a graph is uniquely 2{list colorable if and only if one of its blocks is not a cycle, a complete graph, or a complete bipartite graph. For each k, a uniquely k{list colorable graph is introduced. 

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