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arXiv · 2403.03614

On the mod $k$ chromatic index of graphs

Oothan Nweit·Daqing Yang
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Abstract

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 $χ'_{k}(G) \leq 177k-93$.

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Oothan Nweit, Daqing Yang. 2024-11-07. On the mod $k$ chromatic index of graphs. https://doi.org/10.46298/dmtcs.13187

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