{
  "id": "1008.5361",
  "version": "v1",
  "published": "2010-08-31T16:51:10.000Z",
  "updated": "2010-08-31T16:51:10.000Z",
  "title": "The maximum degree of planar graphs I. Series-parallel graphs",
  "authors": [
    "Michael Drmota",
    "Omer Gimenez",
    "Marc Noy"
  ],
  "comment": "38 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the maximum degree $\\Delta_n$ of a random series-parallel graph with $n$ vertices satisfies $\\Delta_n/\\log n \\to c$ in probability, and $\\mathbb{E}\\, \\Delta_n \\sim c \\log n$ for a computable constant $c>0$. The same result holds for outerplanar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-31T16:51:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum degree",
      "random series-parallel graph",
      "result holds",
      "outerplanar graphs",
      "vertices satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.5361D"
    }
  }
}