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arXiv · 2412.19059

Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable

Ligang Jin·Yingli Kang·Xuding Zhu
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Abstract

The concept of DP-coloring of graphs was introduced by Dvořák and Postle, and was used to prove that planar graphs without cycles of length from $4$ to $8$ are $3$-choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP-$3$-colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable.

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Ligang Jin, Yingli Kang, Xuding Zhu. 2024-12-26. Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable. https://arxiv.org/abs/2412.19059

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