{
  "id": "0809.2335",
  "version": "v5",
  "published": "2008-09-13T12:59:28.000Z",
  "updated": "2011-03-27T11:05:48.000Z",
  "title": "Infinite paths and cliques in random graphs",
  "authors": [
    "A. Berarducci",
    "P. Majer",
    "M. Novaga"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study some percolation problems on the complete graph over $\\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2011-03-27T11:05:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graphs",
      "infinite paths",
      "elementary ergodic theory",
      "sharp sufficient conditions",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2335B"
    }
  }
}