Oothan Nweit ; Daqing Yang - On the mod $k$ chromatic index of graphs

dmtcs:13187 - Discrete Mathematics & Theoretical Computer Science, November 10, 2024, vol. 26:3 - https://doi.org/10.46298/dmtcs.13187
On the mod $k$ chromatic index of graphsArticle

Authors: Oothan Nweit ; Daqing Yang

    For a graph $G$ and an integer $k\geq 2$, a $\chi'_{k}$-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 $\chi'_{k}(G)$ is the minimum number of colors in a $\chi'_{k}$-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 $\chi'_{k}(G)\leq 198k-101$ for every graph $G$. In this paper, we show that $\chi'_{k}(G) \leq 177k-93$.


    Volume: vol. 26:3
    Section: Graph Theory
    Published on: November 10, 2024
    Accepted on: October 24, 2024
    Submitted on: March 7, 2024
    Keywords: Mathematics - Combinatorics

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