Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable
Combinatorics
2024-12-30 v1
Abstract
The concept of DP-coloring of graphs was introduced by Dvo\v{r}\'{a}k and Postle, and was used to prove that planar graphs without cycles of length from to are -choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP--colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length , or are DP-3-colorable.
Keywords
Cite
@article{arxiv.2412.19059,
title = {Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable},
author = {Ligang Jin and Yingli Kang and Xuding Zhu},
journal= {arXiv preprint arXiv:2412.19059},
year = {2024}
}
Comments
27 pages, 11 figures