{
  "id": "1709.04678",
  "version": "v1",
  "published": "2017-09-14T09:23:36.000Z",
  "updated": "2017-09-14T09:23:36.000Z",
  "title": "Enumeration of labelled 4-regular planar graphs",
  "authors": [
    "Marc Noy",
    "Clément Requilé",
    "Juanjo Rué"
  ],
  "comment": "20 pages, 8 figures, 3 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be computed effectively as the solution of a system of equations, from which the coefficients can be extracted. As a byproduct, we also enumerate labelled 3-connected 4-regular planar graphs, and simple 4-regular rooted maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-14T09:23:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar graphs",
      "enumeration",
      "first combinatorial scheme",
      "complete recursive decomposition",
      "exponential generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}