{
  "id": "1105.1764",
  "version": "v1",
  "published": "2011-05-09T19:50:24.000Z",
  "updated": "2011-05-09T19:50:24.000Z",
  "title": "Generating p-extremal graphs",
  "authors": [
    "Derrick Stolee"
  ],
  "comment": "25 pages, 2 figures, 3 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "Define f(n,p) to be the maximum number of edges in a graph on n vertices with p perfect matchings. Dudek and Schmitt proved there exist constants n_p and c_p so that for even n >= n_p, f(n,p) = (n^2)/4+c_p. A graph is p-extremal if it has p perfect matchings and (n^2)/4+c_p edges. Based on Lovasz's Two Ear Theorem and structural results of Hartke, Stolee, West, and Yancey, we develop a computational method for determining c_p and generating the finite set of graphs which describe the infinite family of p-extremal graphs. This method extends the knowledge of the size and structure of p-extremal graphs from p <= 10 to p <= 27. These values provide further evidence towards a conjectured upper bound and prove the sequence c_p is not monotonic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-09T19:50:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C85"
    ],
    "keywords": [
      "generating p-extremal graphs",
      "perfect matchings",
      "maximum number",
      "ear theorem",
      "structural results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1764S"
    }
  }
}