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