{
  "abstract": "Vizing's conjecture, dating back to 1963, asserts that \\[ γ(G\\mathbin{\\square}H) \\geq γ(G)γ(H) \\] for all finite graphs $G$ and $H$, where $γ$ denotes the domination number and $\\square$ denotes the Cartesian product. In 2000, Clark and Suen proved the universal bound \\[ γ(G\\mathbin{\\square}H) \\geq \\frac{1}{2}γ(G)γ(H). \\] Recently, Steiner obtained the first constant-factor improvement of the Clark--Suen bound, proving that \\[ γ(G\\mathbin{\\square}H) \\geq \\frac{5+\\sqrt{73}}{24}γ(G)γ(H) \\approx 0.5643\\,γ(G)γ(H). \\] In this paper, we further improve the universal constant by proving that \\[ γ(G\\mathbin{\\square}H) \\geq \\frac{2}{3}γ(G)γ(H) \\] for all finite graphs $G$ and $H$. Thus, we raise the best known universal constant in the approximate form of Vizing's conjecture from $(5+\\sqrt{73})/24$ to $2/3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.01109",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohsen Aliabadi"
    },
    {
      "name": "Elliot Krop"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07kqhs7nrdw0m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.01109",
  "fulltext_url": null,
  "id": "07kqhs7nrdw0m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.01109",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7167088366",
  "pdf_url": "https://arxiv.org/pdf/2607.01109",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07kqhs7nrdw0m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2607.01109",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.01109"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A $2/3$ Bound for Vizing's Conjecture",
  "title_text": "A 2/3 Bound for Vizing's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/07kqhs7nrdw0m",
  "venue": "arXiv",
  "versions": []
}