Asymptotically the list colouring constants are 1

Authors:
Bruce Reed;Benny Sudakov
Affiliations:
CNRS, Paris, France/ and School of Computer Science, McGill University, Montreal, Canada;Department of Mathematics, Princeton University, Princeton, New Jersey/ and Institute for Advanced Study, Princeton, New Jersey
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

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Abstract

In this paper we prove the following result about vertex list colourings, which shows that a conjecture of the first author (1999, J. Graph Theory 31, 149-153) is asymptotically correct. Let G be a graph with the sets of lists S(υ), satisfying that for every vertex |S(υ)| = (1+o(1))d and for each colour c ∈ S(υ), the number of neighbours of υ that have c in their list is at most d. Then there exists a proper colouring of G from these lists.