{
  "id": "1210.5704",
  "version": "v2",
  "published": "2012-10-21T08:43:54.000Z",
  "updated": "2012-10-23T07:37:04.000Z",
  "title": "Counting graphs with different numbers of spanning trees through the counting of prime partitions",
  "authors": [
    "Jernej Azarija"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let A_n (n >= 1) be the set of all integers x such that there exists a connected graph on n vertices with precisely x spanning trees. In this paper, we show that |A_n| grows faster than sqrt{n}exp(2Pi*sqrt{n/log{n}/Sqrt(3)} This settles a question of Sedlacek.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-23T07:37:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16"
    ],
    "keywords": [
      "spanning trees",
      "prime partitions",
      "counting graphs",
      "grows faster",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5704A"
    }
  }
}