{
  "abstract": "A $d$-simplex-cluster is a collection of $d+1$ distinct $k$-element sets with empty total intersection, nonempty intersection for every $d$ members, and union of size at most $2k$. We prove the simplex-cluster conjecture of Keevash and Mubayi, a common strengthening of the Erdős--Chvátal simplex conjecture and Mubayi's cluster conjecture. More precisely, for integers $k>d\\ge2$ and $n\\ge k(d+1)/d$, every family of $k$-element subsets of an $n$-element set containing no $d$-simplex-cluster has at most $\\binom{n-1}{k-1}$ members. Equality holds if and only if the family consists of all $k$-element subsets containing a fixed point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08567",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongjiang Wu"
    },
    {
      "name": "Lihua Feng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afsgy4egj87s0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08567",
  "fulltext_url": null,
  "id": "afsgy4egj87s0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08567",
  "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": "W7220978116",
  "pdf_url": "https://arxiv.org/pdf/2610.08567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afsgy4egj87s0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Keevash--Mubayi simplex-cluster conjecture",
  "title_text": "The Keevash--Mubayi simplex-cluster conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/afsgy4egj87s0",
  "venue": "arXiv",
  "versions": []
}