{
  "id": "2101.09319",
  "version": "v1",
  "published": "2021-01-22T20:25:18.000Z",
  "updated": "2021-01-22T20:25:18.000Z",
  "title": "On a conjecture of Gross, Mansour and Tucker",
  "authors": [
    "Sergei Chmutov",
    "Fabien Vignes-Tourneret"
  ],
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "Partial duality is a duality of ribbon graphs relative to a subset of their edges generalizing the classical Euler-Poincare duality. This operation often changes the genus. Recently J.L.Gross, T.Mansour, and T.W.Tucker formulated a conjecture that for any ribbon graph different from plane trees and their partial duals, there is a subset of edges partial duality relative to which does change the genus. A family of counterexamples was found by Qi Yan and Xian'an Jin. In this note we prove that essentially these are the only counterexamples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-22T20:25:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C65",
      "57M15",
      "57Q15"
    ],
    "keywords": [
      "conjecture",
      "ribbon graph",
      "qi yan",
      "classical euler-poincare duality",
      "counterexamples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}