{
  "id": "2101.05740",
  "version": "v1",
  "published": "2021-01-14T17:42:00.000Z",
  "updated": "2021-01-14T17:42:00.000Z",
  "title": "Complements of non-separating planar graphs",
  "authors": [
    "Andrei Pavelescu",
    "Elena Pavelescu"
  ],
  "comment": "11 pages, 10 figures",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "We prove that the complement of a non-separating planar graph of order at least nine is intrinsically linked. We also prove that the complement of a non-separating planar graph of order at least 10 is intrinsically knotted. We show these lower bounds on the orders are the best possible. We show that for a maximal non-separating planar graph with $n\\ge 7$ vertices, its complement $cG$ is $(n-7)-$apex. We conclude that the de Verdi\\`ere invariant for such graphs satisfies $\\mu(cG)\\le n-4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-14T17:42:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "complement",
      "maximal non-separating planar graph",
      "lower bounds",
      "graphs satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}