{
  "id": "0912.4670",
  "version": "v3",
  "published": "2009-12-23T15:45:39.000Z",
  "updated": "2010-03-14T18:13:18.000Z",
  "title": "Asymptotic enumeration of labelled graphs with a given genus",
  "authors": [
    "E. A. Bender",
    "Z. Gao"
  ],
  "comment": "28 pages; corrected, clarified & simplified presentation",
  "categories": [
    "math.CO"
  ],
  "abstract": "We enumerate rooted 2-connected and 3-connected surface maps with respect to vertices and edges. We also derive the bivariate version of the large face-width result for random 3-connected maps. These results are then used to derive asymptotic formulas for the number of labelled graphs of genus g (1-connected, 2-connected, and 3-connected graphs.)",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-03-14T18:13:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30"
    ],
    "keywords": [
      "labelled graphs",
      "asymptotic enumeration",
      "large face-width result",
      "bivariate version",
      "surface maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4670B"
    }
  }
}