Geodesic
List coloring of complete multipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 31-37

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The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.
Keywords: list coloring, choice number, complete multipartite graph 
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Vetrík, Tomáš. List coloring of complete multipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 31-37. http://geodesic.mathdoc.fr/item/DMGT_2012_32_1_a2/