{
  "abstract": "Let $F_5$ denote the $3$-uniform hypergraph with edge set $\\{abc,abd,cde\\}$. For a hypergraph property $\\mathcal P$, let $ex_{\\mathcal P}(n,F_5)$ be the maximum number of edges in an $n$-vertex $F_5$-free $3$-uniform hypergraph satisfying $\\mathcal P$. Let $Δ_2(H)$ denote the maximum codegree of a pair of vertices in a $3$-uniform hypergraph $H$. We determine the exact value of $ex_{Δ_2\\ge m}(n,F_5)$ when $m$ is bounded away from $n/3$ by a fixed positive proportion. More precisely, for every constant $c\\in (1/3,1)$, there exists $n_0$ such that for all $n\\ge n_0$ and $m=cn$, \\[ ex_{Δ_2\\ge m}(n,F_5) = m\\left\\lceil\\frac{n-m}{2}\\right\\rceil \\left\\lfloor\\frac{n-m}{2}\\right\\rfloor. \\] The unique extremal hypergraph is the complete tripartite $3$-graph $K^3_{m,\\lceil (n-m)/2\\rceil,\\lfloor (n-m)/2\\rfloor}$. We also prove the corresponding exact result for the blow-ups $F_5^t$, together with stability theorems showing that every near-extremal configuration is close to the relevant tripartite construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12905",
  "author_total": 2,
  "authors": [
    {
      "name": "Yupei Li"
    },
    {
      "name": "Linyuan Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmrx0hze5b9et.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12905",
  "fulltext_url": null,
  "id": "dmrx0hze5b9et",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12905",
  "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": "W7221538797",
  "pdf_url": "https://arxiv.org/pdf/2610.12905",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmrx0hze5b9et.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12905",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12905"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Codegree-Constrained Turán Problems for $F_5$ and Its Blow-ups",
  "title_text": "Codegree-Constrained Turán Problems for F_5 and Its Blow-ups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/dmrx0hze5b9et",
  "venue": "arXiv",
  "versions": []
}