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2021 Planar Graphs Without Pairwise Adjacent $3$-, $4$-, $5$-, and $6$-cycle are $4$-choosable
Kittikorn Nakprasit, Pongpat Sittitrai
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Taiwanese J. Math. Advance Publication 1-23 (2021). DOI: 10.11650/tjm/210701


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.

Funding Statement

This work has received scholarship under the Post-Doctoral Training Program from Khon Kaen University, Thailand. Kittikorn Nakprasit is supported by National Research Council of Thailand and Khon Kaen University under Mid-Career Research Grant (years 2021–2024) in the project of Graph Structural Analysis for Solving Graph Coloring Problems.


The authors would like to thank the referees for their careful reading and valuable suggestions. The authors also would like to express our gratitude to Tao Wang for many important comments pointing out arguments that required some improvement.


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Kittikorn Nakprasit. Pongpat Sittitrai. "Planar Graphs Without Pairwise Adjacent $3$-, $4$-, $5$-, and $6$-cycle are $4$-choosable." Taiwanese J. Math. Advance Publication 1 - 23, 2021.


Published: 2021
First available in Project Euclid: 12 July 2021

Digital Object Identifier: 10.11650/tjm/210701

Primary: 05C10, 05C15

Rights: Copyright © 2021 The Mathematical Society of the Republic of China


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