{
  "id": "1709.00508",
  "version": "v1",
  "published": "2017-09-01T23:37:18.000Z",
  "updated": "2017-09-01T23:37:18.000Z",
  "title": "Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4",
  "authors": [
    "Radoslav Fulek",
    "Jan Kynčl"
  ],
  "comment": "10 pages, 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We find a graph of genus $5$ and its drawing on the orientable surface of genus $4$ with every pair of independent edges crossing an even number of times. This shows that the strong Hanani-Tutte theorem cannot be extended to the orientable surface of genus $4$. As a base step in the construction we use a counterexample to the unified Hanani-Tutte theorem on the torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-01T23:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15"
    ],
    "keywords": [
      "counterexample",
      "strong hanani-tutte theorem",
      "orientable surface",
      "base step",
      "unified hanani-tutte theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}