{
  "id": "2105.02361",
  "version": "v1",
  "published": "2021-05-05T22:44:50.000Z",
  "updated": "2021-05-05T22:44:50.000Z",
  "title": "The ratio of the numbers of odd and even cycles in outerplanar graphs",
  "authors": [
    "Akihiro Higashitani",
    "Naoki Matsumoto"
  ],
  "comment": "16 page, 10 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "In this paper, we investigate the ratio of the numbers of odd and even cycles in outerplanar graphs. We verify that the ratio generally diverges to infinity as the order of a graph diverges to infinity. We also give sharp estimations of the ratio for several classes of outerplanar graphs, and obtain a constant upper bound of the ratio for some of them. Furthermore, we consider similar problems in graphs with some pairs of forbidden subgraphs/minors, and propose a challenging problem concerning claw-free graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-05T22:44:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C31",
      "G.2"
    ],
    "keywords": [
      "outerplanar graphs",
      "constant upper bound",
      "challenging problem concerning claw-free graphs",
      "similar problems",
      "forbidden subgraphs/minors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}