English

Planar graphs without pairwise adjacent 3-,4-,5-, and 6-cycle are 4-choosable

Combinatorics 2019-01-03 v2 Discrete Mathematics

Abstract

Xu and Wu proved that if every 5-cycle of a planar graph G is not simultaneously adjacent to 3-cycles and 4-cycles, then G is 4-choosable. In this paper, we improve this result as follows. If G is a planar graph without pairwise adjacent 3-,4-,5-, and 6-cycle, then G is 4-choosable.

Keywords

Cite

@article{arxiv.1812.10473,
  title  = {Planar graphs without pairwise adjacent 3-,4-,5-, and 6-cycle are 4-choosable},
  author = {Pongpat Sittitrai and Kittikorn Nakprasit},
  journal= {arXiv preprint arXiv:1812.10473},
  year   = {2019}
}

Comments

17 pages and 2 figures

R2 v1 2026-06-23T06:56:40.225Z