{
  "abstract": "For an $r$-uniform hypergraph $H$, let $ν(H)$ be the maximum number of edges no two of which share $r-1$ vertices, and $τ(H)$ the minimum number of $(r-1)$-sets such that every edge contains one of them. Aharoni and Zerbib conjectured that $τ(H)\\le\\lceil\\frac{r+1}{2}\\rceil\\,ν(H)$, which for $r=3$ generalizes Tuza's conjecture on triangles. We prove that the fractional relaxation $τ^*(H)$ of $τ(H)$ satisfies $τ^*(H)\\le\\frac{r+1}{2}\\,ν(H)$. This constant is best possible for every $r$, and for $r\\ge4$ it improves on the previous bound of roughly $3r/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35836",
  "author_total": 1,
  "authors": [
    {
      "name": "Sichen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c25jg3mzkdfg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35836",
  "fulltext_url": null,
  "id": "c25jg3mzkdfg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35836",
  "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": "W7214889657",
  "pdf_url": "https://arxiv.org/pdf/2609.35836",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c25jg3mzkdfg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35836",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35836"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Tight Fractional Version of Generalized Tuza's Conjecture",
  "title_text": "A Tight Fractional Version of Generalized Tuza's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/c25jg3mzkdfg1",
  "venue": "arXiv",
  "versions": []
}