{
  "id": "1811.11873",
  "version": "v1",
  "published": "2018-11-28T23:06:39.000Z",
  "updated": "2018-11-28T23:06:39.000Z",
  "title": "Triangles in $C_5$-free graphs and Hypergraphs of Girth Six",
  "authors": [
    "Beka Ergemlidze",
    "Abhishek Methuku"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new approach and prove that the maximum number of triangles in a $C_5$-free graph on $n$ vertices is at most $$(1 + o(1)) \\frac{1}{3 \\sqrt 2} n^{3/2}.$$ We also show a connection to $r$-uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-28T23:06:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graph",
      "maximum number",
      "uniform hypergraphs",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}