Published online by Cambridge University Press: 12 September 2008
Let G be a graph with maximum degree Δ(G). In this paper we prove that if the girth g(G) of G is greater than 4 then its chromatic number, χ(G), satisfies
where o(l) goes to zero as Δ(G) goes to infinity. (Our logarithms are base e.) More generally, we prove the same bound for the list-chromatic (or choice) number:
provided g(G) < 4.
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