{
  "id": "2008.05186",
  "version": "v1",
  "published": "2020-08-12T09:09:03.000Z",
  "updated": "2020-08-12T09:09:03.000Z",
  "title": "A short proof of the non-biplanarity of $K_9$",
  "authors": [
    "Ahmad Biniaz"
  ],
  "categories": [
    "math.CO",
    "cs.CG",
    "cs.DM"
  ],
  "abstract": "Battle, Harary, and Kodama (1962) and independently Tutte (1963) proved that the complete graph with nine vertices is not biplanar. Aiming towards simplicity and brevity, in this note we provide a short proof of this claim.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-12T09:09:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short proof",
      "non-biplanarity",
      "complete graph",
      "independently tutte"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}