{
  "id": "0803.4418",
  "version": "v2",
  "published": "2008-03-31T10:05:26.000Z",
  "updated": "2008-04-01T12:21:38.000Z",
  "title": "On the number of graphs not containing $K_{3,3}$ as a minor",
  "authors": [
    "S. Gerke",
    "O. Gimenez",
    "M. Noy",
    "A. Weissl"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We derive precise asymptotic estimates for the number of labelled graphs not containing $K_{3,3}$ as a minor, and also for those which are edge maximal. Additionally, we establish limit laws for parameters in random $K_{3,3}$-minor-free graphs, like the expected number of edges. To establish these results, we translate a decomposition for the corresponding graph class into equations for generating functions and use singularity analysis. We also find a precise estimate for the number of graphs not containing the graph $K_{3,3}$ plus an edge as a minor.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-01T12:21:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30"
    ],
    "keywords": [
      "containing",
      "derive precise asymptotic estimates",
      "edge maximal",
      "minor-free graphs",
      "corresponding graph class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.4418G"
    }
  }
}