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arXiv · 1701.09133

The list chromatic number of graphs with small clique number

Michael Molloy
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Abstract

We prove that every triangle-free graph with maximum degree $Δ$ has list chromatic number at most $(1+o(1))\fracΔ{\ln Δ}$. This matches the best-known bound for graphs of girth at least 5. We also provide a new proof that for any $r\geq 4$ every $K_r$-free graph has list-chromatic number at most $200r\frac{Δ\ln\lnΔ}{\lnΔ}$.

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Michael Molloy. 2018-06-29. The list chromatic number of graphs with small clique number. https://arxiv.org/abs/1701.09133

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