List colouring of graphs with at most $\big(2-o(1)\big)\chi$ vertices
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 $$n_0 \leq |V(G) | \le (2-\epsilon)\chi(G).$$
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 2003
- DOI:
- 10.48550/arXiv.math/0304467
- arXiv:
- arXiv:math/0304467
- Bibcode:
- 2003math......4467R
- Keywords:
-
- Combinatorics;
- 05C15;
- 05D40
- E-Print:
- Proceedings of the ICM, Beijing 2002, vol. 3, 587--604