{
  "id": "2403.03614",
  "version": "v2",
  "published": "2024-03-06T11:13:24.000Z",
  "updated": "2024-10-20T11:55:42.000Z",
  "title": "On the mod $k$ chromatic index of graphs",
  "authors": [
    "Oothan Nweit",
    "Daqing Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "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 $\\chi'_{k}(G) \\leq 177k-93$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-10-20T11:55:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic index",
      "minimum number",
      "degrees congruent",
      "graph theory",
      "kohayakawa"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}