{
  "id": "0905.4650",
  "version": "v2",
  "published": "2009-05-28T13:43:04.000Z",
  "updated": "2012-11-08T13:33:17.000Z",
  "title": "Hamilton cycles in random geometric graphs",
  "authors": [
    "József Balogh",
    "Béla Bollobás",
    "Michael Krivelevich",
    "Tobias Müller",
    "Mark Walters"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AAP718 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2011, Vol. 21, No. 3, 1053-1072",
  "doi": "10.1214/10-AAP718",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbor model, there is a constant \\kappa\\ such that almost every \\kappa-connected graph has a Hamilton cycle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-08T13:33:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random geometric graph",
      "hamilton cycle",
      "k-nearest neighbor model",
      "gilbert model",
      "hamiltonian"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4650B"
    }
  }
}