{
  "id": "math/0611842",
  "version": "v1",
  "published": "2006-11-27T23:11:30.000Z",
  "updated": "2006-11-27T23:11:30.000Z",
  "title": "Graphs with restricted valency and matching number",
  "authors": [
    "Niranjan Balachandran",
    "Niraj Khare"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Consider the family of all finite graphs with maximum degree $\\Delta(G)<d$ and matching number $\\nu(G)<m$. In this paper we give a new proof to obtain the exact upper bound for the number of edges in such graphs and also characterize all the cases when the maximal graph is unique. We also provide a new proof of Gallai's lemma concerning factor critical graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-27T23:11:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "matching number",
      "restricted valency",
      "exact upper bound",
      "lemma concerning factor critical graphs",
      "gallais lemma concerning factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11842B"
    }
  }
}