{
  "abstract": "For positive integers $t$ and $q$ let $b_q(t)$ be the smallest integer $n$ so that any coloring of the edges of the complete bipartite graph $K_{n,n}$ with $q$ colors yields a monochromatic copy of $K_{t,t}$. We give an independent proof that $b_2(t)\\le 128\\cdot 2^t$ for every positive integer $t$. More generally, for $0< p\\le 1/2$, every bipartite graph of edge density at least $p$, with both classes of size at least $128\\cdot p^{-t}$, contains $K_{t,t}$. This gives $b_q(t)\\le 128\\cdot q^t$ for every integer $q\\ge 2$ and a uniform consequence for Zarankiewicz numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40288",
  "author_total": 1,
  "authors": [
    {
      "name": "Yury Person"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ybs2x2kxmvm1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40288",
  "fulltext_url": null,
  "id": "9ybs2x2kxmvm1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40288",
  "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": "W7215085003",
  "pdf_url": "https://arxiv.org/pdf/2609.40288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ybs2x2kxmvm1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Another proof that the two color bipartite Ramsey number is $O(2^t)$",
  "title_text": "Another proof that the two color bipartite Ramsey number is O(2^t)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/9ybs2x2kxmvm1",
  "venue": "arXiv",
  "versions": []
}