{
  "id": "2009.05950",
  "version": "v1",
  "published": "2020-09-13T08:24:30.000Z",
  "updated": "2020-09-13T08:24:30.000Z",
  "title": "Counterexamples to the interpolating conjecture on partial-dual genus polynomials of ribbon graphs",
  "authors": [
    "Qi Yan",
    "Xian'an Jin"
  ],
  "comment": "10 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They showed that the partial-dual genus polynomial for an orientable ribbon graph is interpolating and gave an analogous conjecture: The partial-dual Euler-genus polynomial for any non-orientable ribbon graph is interpolating. In this paper, we first give some counterexamples to the conjecture. Then motivated by these counterexamples, we further find two infinite families of counterexamples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-13T08:24:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C30",
      "05C31",
      "57M15"
    ],
    "keywords": [
      "partial-dual genus polynomial",
      "interpolating conjecture",
      "counterexamples",
      "partial-dual euler genus polynomial",
      "partial-dual orientable genus polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}