{
  "id": "1304.5049",
  "version": "v1",
  "published": "2013-04-18T08:27:21.000Z",
  "updated": "2013-04-18T08:27:21.000Z",
  "title": "Maximum degree in minor-closed classes of graphs",
  "authors": [
    "Omer Gimenez",
    "Dieter Mitsche",
    "Marc Noy"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a class of graphs G closed under taking minors, we study the maximum degree \\Delta_n of random graphs from G with n vertices. We prove several lower and upper bounds that hold with high probability. Among other results, we find classes of graphs providing orders of magnitude for \\Delta_n not observed before, such us \\log n/ \\log \\log \\log n and \\log n/ \\log \\log \\log \\log n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-18T08:27:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum degree",
      "minor-closed classes",
      "random graphs",
      "upper bounds",
      "high probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5049G"
    }
  }
}