{
  "abstract": "Let $ν(G)$ be the maximum number of edge-disjoint triangles in a graph $G$ and $τ(G)$ the minimum number of edges meeting every triangle. Tuza conjectured that $τ(G)\\le 2ν(G)$. We prove that $τ(G)\\le (165/59)ν(G)$. The constant $165/59\\approx 2.797$ improves the bound $66/23\\approx 2.870$ that Haxell proved in 1999. The key observation is that, for a suitable red-blue coloring, the families left over in Haxell's construction contain every triangle with exactly one red edge. Such a family $\\mathcal{F}$ admits an exchange that forces certain red edges to lie in a single triangle once the blue edges of a maximum packing are deleted, which gives $τ(\\mathcal{F})\\le (8/3)ν(\\mathcal{F})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13831",
  "author_total": 1,
  "authors": [
    {
      "name": "Sichen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bty5b1ngyfp7r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13831",
  "fulltext_url": null,
  "id": "bty5b1ngyfp7r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13831",
  "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": "W7213269501",
  "pdf_url": "https://arxiv.org/pdf/2609.13831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bty5b1ngyfp7r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Bound Below 2.8 for Tuza's Conjecture",
  "title_text": "A Bound Below 2.8 for Tuza's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bty5b1ngyfp7r",
  "venue": "arXiv",
  "versions": []
}