{
  "id": "1910.03992",
  "version": "v1",
  "published": "2019-10-09T13:54:14.000Z",
  "updated": "2019-10-09T13:54:14.000Z",
  "title": "At least half of the leapfrog fullerene graphs have exponentially many Hamilton cycles",
  "authors": [
    "František Kardoš",
    "Martina Mockovčiaková"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A fullerene graph is a 3-connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the trucation of the dual of the given graph. A fullerene graph is leapfrog if it can be obtained from another fullerene graph by the leapfrog transformation. We prove that leapfrog fullerene graphs on $n=12k-6$ vertices have at least $2^{k}$ Hamilton cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-09T13:54:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "leapfrog fullerene graphs",
      "hamilton cycles",
      "leapfrog transformation",
      "cubic planar graph",
      "planar graph produces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}