English

DP-4-coloring of planar graphs with some restrictions on cycles

Combinatorics 2022-06-13 v2 Discrete Mathematics

Abstract

DP-coloring was introduced by Dvo\v{r}\'{a}k and Postle as a generalization of list coloring. It was originally used to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of lengths 4 to 8 is 3-choosable. In this paper, we give three sufficient conditions for a planar graph to be DP-4-colorable. Actually all the results (Theorem 1.3, 1.4 and 1.7) are stated in the ``color extendability'' form, and uniformly proved by vertex identification and discharging method.

Keywords

Cite

@article{arxiv.1909.08511,
  title  = {DP-4-coloring of planar graphs with some restrictions on cycles},
  author = {Rui Li and Tao Wang},
  journal= {arXiv preprint arXiv:1909.08511},
  year   = {2022}
}

Comments

13 pages, 5 figures. arXiv admin note: text overlap with arXiv:1908.04902