{
  "id": "2212.14323",
  "version": "v1",
  "published": "2022-12-29T14:33:20.000Z",
  "updated": "2022-12-29T14:33:20.000Z",
  "title": "Independence numbers of polyhedral graphs",
  "authors": [
    "Sébastien Gaspoz",
    "Riccardo W. Maffucci"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A polyhedral graph is a $3$-connected planar graph. We find the least possible order $p(k,a)$ of a polyhedral graph containing a $k$-independent set of size $a$ for all positive integers $k$ and $a$. In the case $k = 1$ and $a$ even, we prove that the extremal graphs are exactly the vertex-face (radial) graphs of maximal planar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-29T14:33:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C35",
      "05C10",
      "52B05"
    ],
    "keywords": [
      "independence numbers",
      "maximal planar graphs",
      "independent set",
      "connected planar graph",
      "extremal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}