List colouring of graphs with at most (2-o(1))χ vertices
Bruce Reed, Benny Sudakov
Abstract
Ohba has conjectured ohb that if the graph G has 2χ(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<ε<1, there exist an n0=n0(ε) such that the list chromatic number of G equals its chromatic number, provided n0 ≤ |V(G) | (2-ε)χ(G).
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