{
  "abstract": "In 1977, Erdős posed the problem of determining the maximum number $f_r(n)$ of edges in an $n$-vertex $r$-uniform hypergraph in which all disjoint pairs of edges have distinct unions. Füredi later conjectured that, for every fixed $r\\ge 4$ and all sufficiently large $n$, $f_r(n)=\\binom{n-1}{r-1}+\\lfloor \\frac{n-1}{r}\\rfloor$. In this paper, we prove this conjecture and determine all extremal configurations. Our proof combines a stability theorem for such dense hypergraphs with a delicate deletion argument applied to an associated bipartite $3$-graph. The stability theorem also resolves a conjecture of Mubayi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37744",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Huang"
    },
    {
      "name": "Jie Ma"
    },
    {
      "name": "Tianchi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5sdtwg479q4fs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37744",
  "fulltext_url": null,
  "id": "5sdtwg479q4fs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37744",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214982539",
  "pdf_url": "https://arxiv.org/pdf/2609.37744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5sdtwg479q4fs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal hypergraphs without generalized 4-cycles",
  "title_text": "Extremal hypergraphs without generalized 4-cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5sdtwg479q4fs",
  "venue": "arXiv",
  "versions": []
}