{
  "id": "2310.09973",
  "version": "v1",
  "published": "2023-10-15T22:33:21.000Z",
  "updated": "2023-10-15T22:33:21.000Z",
  "title": "Extending partial edge colorings",
  "authors": [
    "Pál Bärnkopf",
    "Ervin Győri"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the problem of extending partial edge colorings of (iterated) cartesian products of even cycles and paths, focusing on the case when the precolored edges constitute a matching. We prove the conjecture of Casselgren, Granholm and Petros that a precolored distance 3 matching in the Cartesian product of two even cycles can be extended to a 4-coloring of the edge set of the whole graph. Actually, a generalization for the Cartesian product of two bipartite graphs is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-15T22:33:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extending partial edge colorings",
      "cartesian product",
      "edge set",
      "bipartite graphs",
      "precolored edges constitute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}