{
  "abstract": "We prove that there is an absolute positive constant $c$ such that every bipartite graph with $N$ vertices in each part and at least $N^2/2$ edges contains a complete bipartite graph $K_{t,t}$ whenever $N\\ge c\\, 2^{t}$. This improves the classical Kővári-Sós-Turán bound requiring $N$ of order $t\\,2^t $. As a consequence, the diagonal bipartite Ramsey number has upper bound $b(t,t)=O(2^t)$, improving the previous best bound $b(t,t) = O(2^t\\, \\log t )$ due to Conlon. The proof was found by GPT-6 Astra, and the method will probably have further applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32937",
  "author_total": 1,
  "authors": [
    {
      "name": "Dhruv Mubayi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d39gg57vn8nk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32937",
  "fulltext_url": null,
  "id": "4d39gg57vn8nk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32937",
  "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": "W7214749400",
  "pdf_url": "https://arxiv.org/pdf/2609.32937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d39gg57vn8nk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharper Zarankiewicz and Diagonal Bipartite Ramsey Bounds",
  "title_text": "Sharper Zarankiewicz and Diagonal Bipartite Ramsey Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4d39gg57vn8nk",
  "venue": "arXiv",
  "versions": []
}