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Asymptotically the List Colouring Constants Are 1

By Bruce Reed and Benny Sudakov

Abstract

In this paper we prove the following result about vertex list colourings, which shows that a conjecture from [9] is asymptotically correct. Let G be a graph with the sets of lists S(v), satisfying that for every vertex jS(v)j = (1+o(1))d and for each colour c 2 S(v), the number of neighbours of v that have c in their list is at most d. Then there exist a proper colouring of G from these lists

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