{
  "id": "1612.00688",
  "version": "v1",
  "published": "2016-12-02T14:24:05.000Z",
  "updated": "2016-12-02T14:24:05.000Z",
  "title": "Unified Hanani-Tutte theorem",
  "authors": [
    "Radoslav Fulek",
    "Jan Kynčl",
    "Dömötör Pálvölgyi"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We introduce a common generalization of the strong Hanani-Tutte theorem and the weak Hanani-Tutte theorem: if a graph $G$ has a drawing $D$ in the plane where every pair of independent edges crosses an even number of times, then $G$ has a planar drawing preserving the rotation of each vertex that was incident only to even edges in $D$. The theorem is implicit in the proof of the strong Hanani-Tutte theorem by Pelsmajer, Schaefer and \\v{S}tefankovi\\v{c}. We give a new, somewhat simpler proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-02T14:24:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "68R10",
      "G.2.2"
    ],
    "keywords": [
      "unified hanani-tutte theorem",
      "strong hanani-tutte theorem",
      "weak hanani-tutte theorem",
      "somewhat simpler proof",
      "independent edges crosses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}