{
  "id": "2304.02432",
  "version": "v1",
  "published": "2023-04-05T13:31:57.000Z",
  "updated": "2023-04-05T13:31:57.000Z",
  "title": "Large $ Y_{3,2} $-tilings in 3-uniform hypergraphs",
  "authors": [
    "Jie Han",
    "Lin Sun",
    "Guanghui Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $Y_{3,2}$ be the 3-graph with two edges intersecting in two vertices. We prove that every 3-graph $ H $ on $ n $ vertices with at least $ \\max \\left \\{ \\binom{4\\alpha n}{3}, \\binom{n}{3}-\\binom{n-\\alpha n}{3} \\right \\}+o(n^3) $ edges contains a $Y_{3,2}$-tiling covering more than $ 4\\alpha n$ vertices, for sufficiently large $ n $ and $0<\\alpha< 1/4$. The bound on the number of edges is asymptotically best possible and solves a conjecture of the authors for 3-graphs that generalizes the Matching Conjecture of Erd\\H{o}s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-05T13:31:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypergraphs",
      "edges contains",
      "sufficiently large",
      "asymptotically best"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}