{
  "abstract": "A block design is a set family, whose members are called blocks, where every pair of points in the universe is covered by exactly one block. Erdős asked the following question: is it true that if the universe is of size $n$ and each block is of size $Ω(\\sqrt{n})$, then there exists a transversal intersecting every block in $O(1)$ points? We provide a negative answer to this question. Indeed, for arbitrarily large $n$, we construct such a block designs where every transversal intersects some block in $Ω(\\frac{\\log n}{\\log\\log n})$ points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07736",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiaxi Nie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dm674nxpsxnrw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07736",
  "fulltext_url": null,
  "id": "dm674nxpsxnrw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07736",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7212013719",
  "pdf_url": "https://arxiv.org/pdf/2609.07736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dm674nxpsxnrw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Block Designs with Large Transversal-Block Intersections",
  "title_text": "Block Designs with Large Transversal-Block Intersections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dm674nxpsxnrw",
  "venue": "arXiv",
  "versions": []
}