On the mod $k$ chromatic index of graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916477320298496 |
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| author | Nweit, Oothan Yang, Daqing |
| author_facet | Nweit, Oothan Yang, Daqing |
| contents | For a graph $G$ and an integer $k\geq 2$, a $χ'_{k}$-coloring of $G$ is an edge coloring of $G$ such that the subgraph induced by the edges of each color has all degrees congruent to $1 ~ (\mod k)$, and $χ'_{k}(G)$ is the minimum number of colors in a $χ'_{k}$-coloring of $G$. In ["The mod $k$ chromatic index of graphs is $O(k)$", J. Graph Theory. 2023; 102: 197-200], Botler, Colucci and Kohayakawa proved that $χ'_{k}(G)\leq 198k-101$ for every graph $G$. In this paper, we show that $χ'_{k}(G) \leq 177k-93$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the mod $k$ chromatic index of graphs Nweit, Oothan Yang, Daqing Combinatorics For a graph $G$ and an integer $k\geq 2$, a $χ'_{k}$-coloring of $G$ is an edge coloring of $G$ such that the subgraph induced by the edges of each color has all degrees congruent to $1 ~ (\mod k)$, and $χ'_{k}(G)$ is the minimum number of colors in a $χ'_{k}$-coloring of $G$. In ["The mod $k$ chromatic index of graphs is $O(k)$", J. Graph Theory. 2023; 102: 197-200], Botler, Colucci and Kohayakawa proved that $χ'_{k}(G)\leq 198k-101$ for every graph $G$. In this paper, we show that $χ'_{k}(G) \leq 177k-93$. |
| title | On the mod $k$ chromatic index of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.03614 |