2-distance 20-coloring of planar graphs with maximum degree 6
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916299306696704 |
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| author | Aoki, Kengo |
| author_facet | Aoki, Kengo |
| contents | 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 $χ_2(G) \leq 21$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_17191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2-distance 20-coloring of planar graphs with maximum degree 6 Aoki, Kengo Combinatorics 05C15 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 $χ_2(G) \leq 21$. |
| title | 2-distance 20-coloring of planar graphs with maximum degree 6 |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2406.17191 |