{
  "id": "2009.00423",
  "version": "v1",
  "published": "2020-08-30T17:38:34.000Z",
  "updated": "2020-08-30T17:38:34.000Z",
  "title": "Counterexamples to a conjecture of Merker on 3-connected cubic planar graphs with a large cycle spectrum gap",
  "authors": [
    "Carol T. Zamfirescu"
  ],
  "comment": "3 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Merker conjectured that if $k \\ge 2$ is an integer and $G$ a 3-connected cubic planar graph of circumference at least $k$, then the set of cycle lengths of $G$ must contain at least one element of the interval $[k, 2k+2]$. We here prove that for every even integer $k \\ge 6$ there is an infinite family of counterexamples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T17:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C10"
    ],
    "keywords": [
      "large cycle spectrum gap",
      "cubic planar graph",
      "counterexamples",
      "conjecture",
      "cycle lengths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}