{
  "id": "2105.14856",
  "version": "v1",
  "published": "2021-05-31T10:18:11.000Z",
  "updated": "2021-05-31T10:18:11.000Z",
  "title": "3-facial edge-coloring of plane graphs",
  "authors": [
    "Kenny Štorgel",
    "Borut Lužar"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An $\\ell$-facial edge-coloring of a plane graph is a coloring of its edges such that any two edges at distance at most $\\ell$ on a boundary walk of any face receive distinct colors. It is the edge-coloring variant of the $\\ell$-facial vertex coloring, which arose as a generalization of the well-known cyclic coloring. It is conjectured that at most $3\\ell + 1$ colors suffice for an $\\ell$-facial edge-coloring of any plane graph. The conjecture has only been confirmed for $\\ell \\le 2$, and in this paper, we prove its validity for $\\ell = 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-31T10:18:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10"
    ],
    "keywords": [
      "plane graph",
      "face receive distinct colors",
      "colors suffice",
      "well-known cyclic",
      "boundary walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}