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arXiv · 2305.05194

The square of every subcubic planar graph of girth at least 6 is 7-choosable

Seog-Jin Kim·Xiaopan Lian
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Abstract

The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Thomassen (2018) and Hartke, Jahanbekam and Thomas (2016) proved that $\chi(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is whether $\chi_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph. Cranston and Kim (2008) showed that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 7. We prove that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 6.

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Seog-Jin Kim, Xiaopan Lian. 2023-05-09. The square of every subcubic planar graph of girth at least 6 is 7-choosable. https://arxiv.org/abs/2305.05194

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