2-distance 4-coloring of planar subcubic graphs with girth at least 21
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866917950239277056 |
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| author | La, Hoang Montassier, Mickael |
| author_facet | La, Hoang Montassier, Mickael |
| contents | A $2$-distance $k$-coloring of a graph is a proper vertex $k$-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance $4$-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not $2$-distance $4$-colorable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_03587 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | 2-distance 4-coloring of planar subcubic graphs with girth at least 21 La, Hoang Montassier, Mickael Combinatorics Discrete Mathematics A $2$-distance $k$-coloring of a graph is a proper vertex $k$-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance $4$-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not $2$-distance $4$-colorable. |
| title | 2-distance 4-coloring of planar subcubic graphs with girth at least 21 |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2106.03587 |