{
  "id": "2109.10520",
  "version": "v1",
  "published": "2021-09-22T05:26:59.000Z",
  "updated": "2021-09-22T05:26:59.000Z",
  "title": "Note on the Turán number of the $3$-linear hypergraph $C_{13}$",
  "authors": [
    "Shengtong Zhang"
  ],
  "comment": "3 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $C_{13}$ be the $3$-linear hypergraph on $9$ vertices $\\{a,b,c,d,e,f,g,h,i\\}$ with edges $$E = \\{\\{a,b,c\\}, \\{a, d,e\\}, \\{b, f, g\\}, \\{c, h,i\\}\\}.$$ Proving a conjecture of Gy\\'arf\\'as et. al., we show that $$\\text{ex}(n, C_{13}) \\leq \\frac{3n}{2}.$$ This essentially completes the determination of linear Tur\\'an number for $3$-linear hypergraphs with at most $4$ edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-22T05:26:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10"
    ],
    "keywords": [
      "linear hypergraph",
      "turán number",
      "linear turan number",
      "essentially completes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}