{
  "abstract": "We prove that every $4$-partite $4$-uniform hypergraph $H$ with matching number $ν(H)=2$ satisfies $τ(H)\\le 6$, where $τ$ denotes the vertex-cover number. This confirms a claim made by Tuza in his 1979 manuscript but never published with a proof, and closes the case $(r,ν)=(4,2)$ of Ryser's conjecture. The best previous bound was $τ\\le 7$, an integrality consequence of the theorem of Haxell and Scott (2012). The proof uses Gyárfás's intersecting-case theorem ($τ\\le 3$ for intersecting $4$-partite $4$-uniform families), a short projection lemma (four base-disjoint edges in an intersecting family force a two-element cover), and Kőnig's matching theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14281",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrick White"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/92bha9n3c3069.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14281",
  "fulltext_url": null,
  "id": "92bha9n3c3069",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14281",
  "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": "W7213287725",
  "pdf_url": "https://arxiv.org/pdf/2609.14281",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/92bha9n3c3069.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14281",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14281"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tuza's Ryser-conjecture claim for four-partite hypergraphs with matching number two",
  "title_text": "Tuza's Ryser-conjecture claim for four-partite hypergraphs with matching number two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/92bha9n3c3069",
  "venue": "arXiv",
  "versions": []
}