{
  "id": "1810.03299",
  "version": "v1",
  "published": "2018-10-08T07:59:52.000Z",
  "updated": "2018-10-08T07:59:52.000Z",
  "title": "Spanning trees in random graphs",
  "authors": [
    "Richard Montgomery"
  ],
  "comment": "68 pages, 31 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For each $\\Delta>0$, we prove that there exists some $C=C(\\Delta)$ for which the binomial random graph $G(n,C\\log n/n)$ almost surely contains a copy of every tree with $n$ vertices and maximum degree at most $\\Delta$. In doing so, we confirm a conjecture by Kahn.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-08T07:59:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spanning trees",
      "binomial random graph",
      "maximum degree",
      "surely contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}