{
  "id": "1207.0996",
  "version": "v2",
  "published": "2012-07-04T14:33:22.000Z",
  "updated": "2015-02-10T13:27:14.000Z",
  "title": "The maximum number of intersections of two polygons",
  "authors": [
    "Felix Günther"
  ],
  "comment": "This paper has been withdrawn by the author due to an unrecoverable error in the proof of Lemma 2. In fact, a counterexample to an even weaker version of Lemma 2 has been found by the author",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p and q are both odd and both polygons are simple, the problem is more difficult. The conjectured maximum is (p-1)(q-1)+2 for all odd p and q.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-04T14:33:22.000Z",
      "abstract": "We determine the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p and q are both odd and both polygons are simple, the problem is more difficult. We prove that the conjectured maximum (p-1)(q-1)+2 is correct for all odd p and q.",
      "comment": "7 pages, 5 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-10T13:27:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C45"
    ],
    "keywords": [
      "maximum number",
      "intersections",
      "conjectured maximum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0996G"
    }
  }
}