{
  "id": "1908.05481",
  "version": "v1",
  "published": "2019-08-15T10:27:32.000Z",
  "updated": "2019-08-15T10:27:32.000Z",
  "title": "Planar cubic graphs of small diameter",
  "authors": [
    "Kolja Knauer",
    "Piotr Micek"
  ],
  "comment": "2 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Cubic planar $n$-vertex graphs with faces of length at most $6$, e.g., fullerene graphs, have diameter in $\\Omega(\\sqrt{n})$. It has been suspected, that a similar result can be shown for cubic planar graphs with faces of bounded length. This note provides a family of cubic planar $n$-vertex graphs with faces of length at most $7$ and diameter in ${O}(\\log n)$, thus refuting the above suspicion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-15T10:27:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar cubic graphs",
      "small diameter",
      "vertex graphs",
      "cubic planar graphs",
      "fullerene graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}