{
  "id": "0710.2995",
  "version": "v1",
  "published": "2007-10-16T09:39:11.000Z",
  "updated": "2007-10-16T09:39:11.000Z",
  "title": "On the growth rate of minor-closed classes of graphs",
  "authors": [
    "Olivier Bernardi",
    "Marc Noy",
    "Dominic Welsh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which have $n$ vertices. A recent result of Norine et al. shows that for all minor-closed class $C$, there is a constant $r$ such that $c_n < r^n n!$. Our main results show that the growth rate of $c_n$ is far from arbitrary. For example, no minor-closed class $C$ has $c_n= r^{n+o(n)} n!$ with $0 < r < 1$ or $1 < r < \\xi \\approx 1.76$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-16T09:39:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C83",
      "05C30"
    ],
    "keywords": [
      "growth rate",
      "minor-closed classes",
      "main results",
      "labelled graphs",
      "isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2995B"
    }
  }
}