{
  "abstract": "For a family $\\mathcal{F}$ of $k$-graphs, $ex_k(n,\\mathcal{F})$ denotes the maximum number of edges in an $n$-vertex $\\mathcal{F}$-free $k$-graph. Let $M_{s+1}^k$ denote a matching of size $s+1$ in $k$-uniform hypergraphs. Recently, Alon and Frankl (JCTB, 2024) determined $ex_2(n,\\{M_{s+1}^2,K_{\\ell+1}\\})$ for all $n\\geq 2s+1$ and $\\ell\\geq 2$. For every non-bipartite graph $F$, Gerbner (JGT, 2024) determined $ex_2(n,\\{M_{s+1}^2,F\\})$ for sufficiently large $n$. In this paper, we investigate this problem for different ranges of the matching parameter. First we prove that for every graph $F$ with $χ(F)>3$, there exist constants $β>0$ and $s_0$ such that $ex_2(n,\\{M^2_{s+1}, F\\})=ex_2(2s+1,F)$ for $\\max\\{s_0,n/2-βn\\}<s<n/2$. For integers $\\ell\\ge k\\ge3$, let $\\mathcal{K}_{\\ell+1}^k$ be the family of all $k$-graphs $F$ with at most $\\binom{\\ell+1}{2}$ edges for which there is an $(\\ell+1)$-set $L$ such that every pair of vertices of $L$ is covered by an edge of $F$, and let $H_{\\ell+1}^k$ be the $k$-uniform hypergraph obtained from the complete graph $K_{\\ell+1}$ by enlarging each edge with a set of $k-2$ new vertices, which is a member of $\\mathcal{K}_{\\ell+1}^k$. We determine $ex_k\\bigl(n,\\mathcal{K}_{\\ell+1}^k\\cup\\{M_{s+1}^k\\}\\bigr)$ for $s< \\frac{n}{8(k-1)^{k-2}(\\ell-1)^3}$. For sufficiently large $s$, we also determine $ex_k\\bigl(n,\\{M_{s+1}^k,H_{\\ell+1}^k\\}\\bigr)$ for $\\frac{n}{k}-βn<s\\leq \\frac{n-k}{k}$ and $s< \\frac{n}{8(k-1)^{k-2}(\\ell-1)^3}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24353",
  "author_total": 3,
  "authors": [
    {
      "name": "Jialin Liu"
    },
    {
      "name": "Mingyang Guo"
    },
    {
      "name": "Xiumei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68fz2qy3wq80s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24353",
  "fulltext_url": null,
  "id": "68fz2qy3wq80s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24353",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214008452",
  "pdf_url": "https://arxiv.org/pdf/2609.24353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68fz2qy3wq80s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2609.24353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Turán problems with bounded matching number in $k$-uniform hypergraphs",
  "title_text": "Turán problems with bounded matching number in k-uniform hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/68fz2qy3wq80s",
  "venue": "arXiv",
  "versions": []
}