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arXiv · 2406.17191

2-distance 20-coloring of planar graphs with maximum degree 6

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, denoted by $χ_2(G)$. In this paper, we show that $χ_2(G) \leq 20$ for every planar graph $G$ with maximum degree at most six, which improves a former bound $χ_2(G) \leq 21$.

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Kengo Aoki. 2024-06-25. 2-distance 20-coloring of planar graphs with maximum degree 6. https://arxiv.org/abs/2406.17191

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