{
  "id": "1203.3079",
  "version": "v2",
  "published": "2012-03-14T13:18:15.000Z",
  "updated": "2014-01-10T20:13:33.000Z",
  "title": "On the diameter of random planar graphs",
  "authors": [
    "Guillaume Chapuy",
    "Éric Fusy",
    "Omer Giménez",
    "Marc Noy"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the diameter D(G_n) of a random labelled connected planar graph with n vertices is equal to n^{1/4+o(1)}, in probability. More precisely there exists a constant c>0 such that the probability that D(G_n) lies in the interval (n^{1/4-\\epsilon},n^{1/4+\\epsilon}) is greater than 1-\\exp(-n^{c\\epsilon}) for {\\epsilon} small enough and n>n_0(\\epsilon). We prove similar statements for 2-connected and 3-connected planar graphs and maps.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-10T20:13:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random planar graphs",
      "random labelled connected planar graph",
      "probability",
      "similar statements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.3079C"
    }
  }
}