{
  "abstract": "A set pair system $\\{(A_i,B_i)\\}_{i=1}^m$ is $1$-cross intersecting if $|A_i \\cap B_i|=0$ for all $i$ and $|A_i \\cap B_j| = 1$ whenever $i \\neq j$. Let $m(a,b,1)$ denote the maximum size $m$ of a $1$-cross intersecting set pair system $\\{(A_i,B_i)\\}_{i=1}^m$ where $|A_i| \\leq a$ and $|B_i| \\leq b$ for all $i$. We prove a conjecture of Füredi, Gyárfás, and Király [Combin. Probab. Comput. 32 (2023)] that asserts $m(n,n,1)/\\binom{2n}{n} \\to 0$ as $n \\to \\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23891",
  "author_total": 3,
  "authors": [
    {
      "name": "Dylan King"
    },
    {
      "name": "Van Magnan"
    },
    {
      "name": "Cory Palmer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/468saxrjtcke1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23891",
  "fulltext_url": null,
  "id": "468saxrjtcke1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23891",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214016507",
  "pdf_url": "https://arxiv.org/pdf/2609.23891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/468saxrjtcke1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "$1$-cross intersecting set pair systems are small",
  "title_text": "$1$-cross intersecting set pair systems are small",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/468saxrjtcke1",
  "venue": "arXiv",
  "versions": []
}