{
  "id": "1001.3628",
  "version": "v1",
  "published": "2010-01-20T16:08:13.000Z",
  "updated": "2010-01-20T16:08:13.000Z",
  "title": "Asymptotic enumeration and limit laws for graphs of fixed genus",
  "authors": [
    "Guillaume Chapuy",
    "Eric Fusy",
    "Omer Gimenez",
    "Bojan Mohar",
    "Marc Noy"
  ],
  "journal": "Journal of Combinatorial Theory, Series A, 118(3):748-777 (2011)",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is shown that the number of labelled graphs with n vertices that can be embedded in the orientable surface S_g of genus g grows asymptotically like $c^{(g)}n^{5(g-1)/2-1}\\gamma^n n!$ where $c^{(g)}>0$, and $\\gamma \\approx 27.23$ is the exponential growth rate of planar graphs. This generalizes the result for the planar case g=0, obtained by Gimenez and Noy. An analogous result for non-orientable surfaces is obtained. In addition, it is proved that several parameters of interest behave asymptotically as in the planar case. It follows, in particular, that a random graph embeddable in S_g has a unique 2-connected component of linear size with high probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-20T16:08:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit laws",
      "asymptotic enumeration",
      "fixed genus",
      "planar case",
      "exponential growth rate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.3628C"
    }
  }
}