{
  "id": "1308.4613",
  "version": "v1",
  "published": "2013-08-21T15:27:42.000Z",
  "updated": "2013-08-21T15:27:42.000Z",
  "title": "Random subtrees of complete graphs",
  "authors": [
    "Alex J. Chin",
    "Gary Gordon",
    "Kellie J. MacPhee",
    "Charles Vincent"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the asymptotic behavior of four statistics associated with subtrees of complete graphs: the uniform probability $p_n$ that a random subtree is a spanning tree of $K_n$, the weighted probability $q_n$ (where the probability a subtree is chosen is proportional to the number of edges in the subtree) that a random subtree spans and the two expectations associated with these two probabilities. We find $p_n$ and $q_n$ both approach $e^{-e^{-1}}\\approx .692$, while both expectations approach the size of a spanning tree, i.e., a random subtree of $K_n$ has approximately $n-1$ edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-21T15:27:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "complete graphs",
      "spanning tree",
      "random subtree spans",
      "asymptotic behavior",
      "uniform probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4613C"
    }
  }
}