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arXiv · 2303.07901

Weak degeneracy of planar graphs and locally planar graphs

Ming Han·Tao Wang·Jianglin Wu·Huan Zhou·Xuding Zhu
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Abstract

Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d + 1)$-list assignment $L$ of $G$, one can construct an $L$-coloring of $G$ by a modified greedy coloring algorithm. It is known that planar graphs of girth 5 are 3-choosable and locally planar graphs are 5-choosable. This paper strengthens these results and proves that planar graphs of girth 5 are weakly 2-degenerate and locally planar graphs are weakly 4-degenerate.

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Ming Han, Tao Wang, Jianglin Wu, Huan Zhou, Xuding Zhu. 2023-03-14. Weak degeneracy of planar graphs and locally planar graphs. https://arxiv.org/abs/2303.07901

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