{
  "id": "2305.01193",
  "version": "v1",
  "published": "2023-05-02T04:01:15.000Z",
  "updated": "2023-05-02T04:01:15.000Z",
  "title": "Wickets in 3-uniform Hypergraphs",
  "authors": [
    "Jozsef Solymosi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In these notes, we consider a Tur\\'an-type problem in hypergraphs. What is the maximum number of edges if we forbid a subgraph? Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, called {\\em wicket}, is formed by three rows and two columns of a $3 \\times 3$ point matrix. We describe two linear hypergraphs -- both containing a wicket -- that if we forbid either of them in $H_n^{(3)}$, then the hypergraph is sparse, and the number of its edges is $o(n^2)$. This proves a conjecture of Gy\\'arf\\'as and S\\'ark\\\"ozy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T04:01:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear hypergraph",
      "turan-type problem",
      "maximum number",
      "vertex common",
      "special hypergraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}