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arXiv · 1811.02920

DP-4-colorability of two classes of planar graphs

Lily Chen·Runrun Liu·Gexin Yu·Ren Zhao·Xiangqian Zhou
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Abstract

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). In this paper, we prove that every planar graph $G$ without $4$-cycles adjacent to $k$-cycles is DP-$4$-colorable for $k=5$ and $6$. As a consequence, we obtain two new classes of $4$-choosable planar graphs. We use identification of verticec in the proof, and actually prove stronger statements that every pre-coloring of some short cycles can be extended to the whole graph.

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Lily Chen, Runrun Liu, Gexin Yu, Ren Zhao, Xiangqian Zhou. 2018-11-07. DP-4-colorability of two classes of planar graphs. https://arxiv.org/abs/1811.02920

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