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List coloring triangle-free planar graphs

Authors:	Jianzhang Hu Xuding Zhu

Affiliation:	Department of Mathematics, Zhejiang Normal University, Jinhua, China

Abstract:	This paper proves the following result. Assume $G$ is a triangle-free planar graph, $X$ is an independent set of $G$ . If $L$ is a list assignment of $G$ such that $◂=▸ \| L (v) \| = 4$ for each vertex $◂+▸ v \in V (G) - X$ and $◂=▸ \| L (v) \| = 3$ for each vertex $v \in X$ , then $G$ is $L$ -colorable.

Keywords:	list coloring planar graphs triangle free