Some results on 2-distance coloring of planar graphs with girth five
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908495709732864 |
|---|---|
| author | Deniz, Zakir |
| author_facet | Deniz, Zakir |
| contents | A vertex coloring of a graph $G$ is called a 2-distance coloring if any two vertices at a distance at most $2$ from each other receive different colors. Suppose that $G$ is a planar graph with girth $5$ and maximum degree $Δ$. We prove that $G$ admits a $2$-distance $Δ+7$ coloring, which improves the result of Dong and Lin (J. Comb. Optim. 32(2), 645-655, 2016). Moreover, we prove that $G$ admits a $2$-distance $Δ+6$ coloring when $Δ\geq 10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00390 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some results on 2-distance coloring of planar graphs with girth five Deniz, Zakir Combinatorics 05C15 A vertex coloring of a graph $G$ is called a 2-distance coloring if any two vertices at a distance at most $2$ from each other receive different colors. Suppose that $G$ is a planar graph with girth $5$ and maximum degree $Δ$. We prove that $G$ admits a $2$-distance $Δ+7$ coloring, which improves the result of Dong and Lin (J. Comb. Optim. 32(2), 645-655, 2016). Moreover, we prove that $G$ admits a $2$-distance $Δ+6$ coloring when $Δ\geq 10$. |
| title | Some results on 2-distance coloring of planar graphs with girth five |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2308.00390 |