List $4$-colouring of planar graphs

Xuding Zhu

List $4$-colouring of planar graphs

Combinatorics 2022-05-25 v3

Authors: Xuding Zhu

Abstract

This paper proves the following result: If $G$ is a planar graph and $L$ is a $4$ -list assignment of $G$ such that $|L(x) \cap L(y)| \le 2$ for every edge $xy$ , then $G$ is $L$ -colourable. This answers a question asked by Kratochv\'{i}l, Tuza and Voigt in [Journal of Graph Theory, 27(1):43--49, 1998].

Keywords

planar graphs list coloring 4-list assignment L-colourable graph theory

Cite

@article{arxiv.2203.16314,
  title  = {List $4$-colouring of planar graphs},
  author = {Xuding Zhu},
  journal= {arXiv preprint arXiv:2203.16314},
  year   = {2022}
}

Comments

11 pages

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