{
  "id": "1605.05764",
  "version": "v1",
  "published": "2016-05-18T21:47:56.000Z",
  "updated": "2016-05-18T21:47:56.000Z",
  "title": "Packing arborescences in random digraphs",
  "authors": [
    "Carlos Hoppen",
    "Roberto F. Parente",
    "Cristiane M. Sato"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We study the problem of packing arborescences in the random digraph $\\mathcal D(n,p)$, where each possible arc is included uniformly at random with probability $p=p(n)$. Let $\\lambda(\\mathcal D(n,p))$ denote the largest integer $\\lambda\\geq 0$ such that, for all $0\\leq \\ell\\leq \\lambda$, we have $\\sum_{i=0}^{\\ell-1} (\\ell-i)|\\{v: d^{in}(v) = i\\}| \\leq \\ell$. We show that the maximum number of arc-disjoint arborescences in $\\mathcal D(n,p)$ is $\\lambda(\\mathcal D(n,p))$ a.a.s. We also give tight estimates for $\\lambda(\\mathcal D(n,p))$ depending on the range of $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-18T21:47:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C80",
      "05D40",
      "05C05",
      "05C35"
    ],
    "keywords": [
      "random digraph",
      "packing arborescences",
      "largest integer",
      "maximum number",
      "arc-disjoint arborescences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}