{
  "id": "1905.07913",
  "version": "v1",
  "published": "2019-05-20T07:06:42.000Z",
  "updated": "2019-05-20T07:06:42.000Z",
  "title": "Variations on the Petersen colouring conjecture",
  "authors": [
    "François Pirot",
    "Jean-Sébastien Sereni",
    "Riste Škrekovski"
  ],
  "comment": "Submitted to a journal on February, 15th 2019",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with $5$ colours such that for every edge $e$, the set of colours assigned to the edges adjacent to $e$ has cardinality either $2$ or $4$, but not $3$. We prove that every bridgeless cubic graph $G$ admits an edge-colouring with $4$ colours such that at most $\\frac45\\cdot|V(G)|$ edges do not satisfy the above condition. This bound is tight and the Petersen graph is the only connected graph for which the bound cannot be decreased. We obtain such a $4$-edge-colouring by using a carefully chosen subset of edges of a perfect matching, and the analysis relies on a simple discharging procedure with essentially no reductions and very few rules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T07:06:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "variations",
      "bridgeless cubic graph admits",
      "petersen colouring conjecture states",
      "simple discharging procedure",
      "edges adjacent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}