{
  "id": "math/0609802",
  "version": "v1",
  "published": "2006-09-28T13:13:43.000Z",
  "updated": "2006-09-28T13:13:43.000Z",
  "title": "The probability that a random multigraph is simple",
  "authors": [
    "Svante Janson"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Consider a random multigraph G* with given vertex degrees d_1,...,d_n, contructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges (d_1+...+d_n)/2 tending to infinity, the probability that the multigraph is simple stays away from 0 if and only if \\sum d_i^2=O(\\sum d_i). This was previously known only under extra assumtions on the maximum degree. We also give an asymptotic formula for this probability, extending previous results by several authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-28T13:13:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C30",
      "60C05"
    ],
    "keywords": [
      "random multigraph",
      "probability",
      "simple stays away",
      "vertex degrees",
      "configuration model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9802J"
    }
  }
}