On uniquely list colorable graphs

Details On uniquely list colorable graphs On uniquely list colorable graphs

1999-06-02

arxiv.org/abs/math/9906009v1

Ars Combinatoria 59 (2001), 307-318

Mathematics

Combinatorics

13 pages

Scientific paper

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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