Planar Graphs Without Pairwise Adjacent $3$-, $4$-, $5$-, and $6$-cycle are $4$-choosable
Kittikorn Nakprasit, Pongpat Sittitrai · Taiwanese Journal of Mathematics · 2021
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.