{
  "id": "2106.00381",
  "version": "v1",
  "published": "2021-06-01T10:43:51.000Z",
  "updated": "2021-06-01T10:43:51.000Z",
  "title": "On an open problem and a conjecture of GROSS, MANSOUR and TUCKER",
  "authors": [
    "Qiyao Chen",
    "Yichao Chen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, Gross, Mansour and Tucker introduced the partial-twuality polynomials. In this paper, we find that when there are enough parallel edges, any multiple graph is a negative answer to the problem 8.7 in their paper [European J. Combin. 95 (2021), 103329]: Is the restricted-orientable partial-Petrial polynomial of an arbitrary ribbon graph even-interpolating? In addition, we also find a counterexample to the conjecture 8.1 of Gross, Mansour and Tucker: If the partial-dual genus polynomial is neither an odd nor an even polynomial, then it is interpolating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-01T10:43:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open problem",
      "conjecture",
      "partial-dual genus polynomial",
      "restricted-orientable partial-petrial polynomial",
      "partial-twuality polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}