{
  "id": "2312.13638",
  "version": "v1",
  "published": "2023-12-21T08:03:45.000Z",
  "updated": "2023-12-21T08:03:45.000Z",
  "title": "Colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson",
  "authors": [
    "Ján Karabáš",
    "Edita Máčajová",
    "Roman Nedela",
    "Martin Škoviera"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new invariant of a cubic graph - its regular defect - which is defined as the smallest number of edges left uncovered by any collection of three perfect matchings that have no edge in common. This invariant is a modification of defect, an invariant introduced by Steffen (J. Graph Theory 78 (2015), 195--206), whose definition does not require the empty intersection condition. In this paper we discuss the relationship of this invariant to the well-known conjectures of Fulkerson (1971) and Fan and Raspaud (1994) and prove that defect and regular defect can be arbitrarily far apart.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-21T08:03:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C70"
    ],
    "keywords": [
      "cubic graph",
      "colouring defect",
      "fan-raspaud",
      "regular defect",
      "empty intersection condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}