{
  "abstract": "For a fixed graph $G$, an $r$-uniform hypergraph is said to contain a Berge-$G$ if there exists a bijection $f\\colon E(G)\\to E(\\mathcal{H})$ for some subhypergraph $\\mathcal{H}$ such that $e\\subseteq f(e)$ for every $e\\in E(G)$. Motivated by Alon and Frankl's study of Turán problems under bounded matching constraints, we investigate the maximum number of edges in $r$-uniform Berge-$K_3$-free hypergraphs with matching number at most~$s$. We determine the exact Turán numbers for the cases $r=3$ and $r=4$. For $r=3$ and $n \\geq 3 s$, we prove that every $n$-vertex Berge- $K_3$-free 3-graph with matching number $s$ has at most $s(n-2 s)$ edges, and we characterize the unique extremal hypergraph attaining equality. For $r=4$ and $n \\geq 4 s$, the maximum number of edges is $s\\lfloor(n-2 s) / 2\\rfloor$, except for the exceptional case $s=1$ and $n \\equiv 1(\\bmod 4)$, in which the bound is $(n-1) / 2$. As a corollary, our results recover the classical theorem of Győri on Berge-$K_3$-free hypergraphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12300",
  "author_total": 3,
  "authors": [
    {
      "name": "Yue Xu"
    },
    {
      "name": "Jiasheng Zeng"
    },
    {
      "name": "Xiao-Dong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7sse66vyfat4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12300",
  "fulltext_url": null,
  "id": "f7sse66vyfat4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12300",
  "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": "W7168429218",
  "pdf_url": "https://arxiv.org/pdf/2607.12300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7sse66vyfat4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2607.12300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12300"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Turán number of a matching and a Berge triangle",
  "title_text": "Turán number of a matching and a Berge triangle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/f7sse66vyfat4",
  "venue": "arXiv",
  "versions": []
}