{
  "id": "1110.4310",
  "version": "v1",
  "published": "2011-10-19T15:25:43.000Z",
  "updated": "2011-10-19T15:25:43.000Z",
  "title": "On graphs having maximal independent sets of exactly $t$ distinct cardinalities",
  "authors": [
    "Bert L. Hartnell",
    "Douglas F. Rall"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a given positive integer t we consider graphs having maximal independent sets of precisely t distinct cardinalities and restrict our attention to those that have no vertices of degree one. In the situation when t is four or larger and the length of the shortest cycle is at least 6t-6, we completely characterize such graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-19T15:25:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C38"
    ],
    "keywords": [
      "maximal independent sets",
      "distinct cardinalities",
      "shortest cycle",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.4310H"
    }
  }
}