English

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 44 to 88 are 33-choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP-33-colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length 44, 66 or 88 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