List colouring of graphs with at most $\big(2-o(1)\big)\chi$ vertices

Bruce Reed; Benny Sudakov

List colouring of graphs with at most $\big(2-o(1)\big)\chi$ vertices

Combinatorics 2007-05-23 v1

Authors: Bruce Reed , Benny Sudakov

Abstract

Ohba has conjectured \cite{ohb} that if the graph $G$ has $2\chi(G)+1$ or fewer vertices then the list chromatic number and chromatic number of $G$ are equal. In this paper we prove that this conjecture is asymptotically correct. More precisely we obtain that for any $0<\epsilon<1$ , there exist an $n_0=n_0(\epsilon)$ such that the list chromatic number of $G$ equals its chromatic number, provided $n_0 \leq |V(G) | \le (2-\epsilon)\chi(G).$

Keywords

list coloring chromatic number list chromatic number ohba conjecture graph coloring asymptotic bounds

Cite

@article{arxiv.math/0304467,
  title  = {List colouring of graphs with at most $\big(2-o(1)\big)\chi$ vertices},
  author = {Bruce Reed and Benny Sudakov},
  journal= {arXiv preprint arXiv:math/0304467},
  year   = {2007}
}

List colouring of graphs with at most $\big(2-o(1)\big)\chi$ vertices

Abstract

Keywords

Cite

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