List Coloring of Random and Pseudo-Random Graphs

choice number

of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n, p(n)) is almost surely whenever . A related result for pseudo-random graphs is proved as well. By a special case of this result, the choice number (as well as the chromatic number) of any graph on n vertices with minimum degree at least in which no two distinct vertices have more than common neighbors is at most .

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Received: October 13, 1997

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Alon, N., Krivelevich, M. & Sudakov, B. List Coloring of Random and Pseudo-Random Graphs. Combinatorica 19, 453–472 (1999).

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  • AMS Subject Classification (1991) Classes:  05C80, 05C15