{
  "id": "1504.00769",
  "version": "v1",
  "published": "2015-04-03T08:02:09.000Z",
  "updated": "2015-04-03T08:02:09.000Z",
  "title": "The maximal length of a gap between r-graph Turán densities",
  "authors": [
    "Oleg Pikhurko"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Tur\\'an density $\\pi(\\cal F)$ of a family $\\cal F$ of $r$-graphs is the limit as $n\\to\\infty$ of the maximum edge density of an $\\cal F$-free $r$-graph on $n$ vertices. Erdos [Israel J. Math 2 (1964) 183--190] proved that no Tur\\'an density can lie in the open interval $(0,r!/r^r)$. Here we show that any other open subinterval of $[0,1]$ avoiding Tur\\'an densities has strictly smaller length. In particular, this implies a conjecture of Grosu [E-print arXiv:1403.4653v1, 2014].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-03T08:02:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "r-graph turán densities",
      "maximal length",
      "turan density",
      "maximum edge density",
      "open interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400769P"
    }
  }
}