{
  "abstract": "Let $m(k,b)$ denote the minimum number of edges in an intersecting $k$-uniform hypergraph in which every $(k-1)$-set of vertices is disjoint from at least $b$ edges, with $m(k,b)=+\\infty$ if no such hypergraph exists. Duke and Erdős [Congressus Numerantium (1980)] asked whether $m(k,k)=o(k^4)$ is possible. In this paper, we answer this question affirmatively and determine the order of growth of $m(k,k)$ by proving that $k^2+1\\leq m(k,k)\\leq Ck^2$ for all sufficiently large $k$, where $C$ is an absolute constant. More generally, we show that $m(k,b)=Θ(kb)$ for all sufficiently large odd $k$ and every integer $b$ with $k\\leq b\\leq (k-1)(k-3)/2$, where the implied constants are independent of $k$ and $b$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01915",
  "author_total": 3,
  "authors": [
    {
      "name": "Guoqing Wang"
    },
    {
      "name": "Linlin Wang"
    },
    {
      "name": "Jun Yue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0bpekj0gj0wyw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01915",
  "fulltext_url": null,
  "id": "0bpekj0gj0wyw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01915",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0bpekj0gj0wyw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Quadratic bounds for intersecting hypergraphs: An affirmative answer to a question of Duke and Erdős",
  "title_text": "Quadratic bounds for intersecting hypergraphs: An affirmative answer to a question of Duke and Erdős",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0bpekj0gj0wyw",
  "venue": "arXiv",
  "versions": []
}