{
  "id": "1301.1521",
  "version": "v2",
  "published": "2013-01-08T13:24:41.000Z",
  "updated": "2013-06-05T14:53:57.000Z",
  "title": "On the excessive [m]-index of a tree",
  "authors": [
    "Giuseppe Mazzuoccolo"
  ],
  "comment": "12 pages, 7 figures, to appear in Discrete Applied Mathematics",
  "categories": [
    "math.CO"
  ],
  "abstract": "The excessive [m]-index of a graph G is the minimum number of matchings of size m needed to cover the edge-set of G. We call a graph G [m]-coverable if its excessive [m]-index is finite. Obviously the excessive [1]-index is |E(G)| for all graphs and it is an easy task the computation of the excessive [2]-index for a [2]-coverable graph. The case m=3 is completely solved by Cariolaro and Fu in 2009. In this paper we prove a general formula to compute the excessive [4]-index of a tree and we conjecture a possible generalization for any value of m. Furthermore, we prove that such a formula does not work for the excessive [4]-index of an arbitrary graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-05T14:53:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C15"
    ],
    "keywords": [
      "minimum number",
      "general formula",
      "arbitrary graph",
      "computation",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1521M"
    }
  }
}