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arXiv · 2308.01824

Square Coloring of Planar Graphs with Maximum Degree at Most Five

Jiani Zou·Miaomiao Han·Hong-Jian Lai
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Abstract

The \textit{square} of a graph $G$, denoted by $G^2$, is obtained from $G$ by adding an edge to connect every pair of vertices with a common neighbor in $G$. In this paper we prove that for every planar graph $G$ with maximum degree at most $5$, $G^2$ admits a proper vertex coloring using at most $17$ colors, which improves the upper bound $18$ recently obtained by Hou, Jin, Miao, and Zhao.

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Jiani Zou, Miaomiao Han, Hong-Jian Lai. 2023-08-13. Square Coloring of Planar Graphs with Maximum Degree at Most Five. https://arxiv.org/abs/2308.01824

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