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arXiv · 2307.16394

Improved 2-Distance Coloring of Planar Graphs with Maximum Degree 5

Kengo Aoki
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Abstract

A 2-distance $k$-coloring of a graph $G$ is a proper $k$-coloring such that any two vertices at distance two or less get different colors. The 2-distance chromatic number of $G$ is the minimum $k$ such that $G$ has a 2-distance $k$-coloring, denote as $χ_2(G)$. In this paper, we show that $χ_2(G) \leq 17$ for every planar graph $G$ with maximum degree $Δ\leq 5$, which improves a former bound $χ_2(G) \leq 18$.

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Kengo Aoki. 2023-07-31. Improved 2-Distance Coloring of Planar Graphs with Maximum Degree 5. https://arxiv.org/abs/2307.16394

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