{
  "abstract": "Let $R_r(k)$ denote the diagonal $r$-colour Ramsey number. We prove that there exist absolute constants $c,K>0$ such that $R_r(k)\\le r^{rk}\\exp\\!\\left(-c\\frac{k}{r\\log^2(2r)}\\right)$ for every $r\\ge2$ and every $k\\ge Kr^2\\log^6(2r)$. This improves the exponential saving in a recent bound of Yang and Mao by a factor of order $r\\log^2(2r)$. The proof proceeds through an off-diagonal bound, which asymptotically improves the classical multinomial bound throughout a neighbourhood of the diagonal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04596",
  "author_total": 1,
  "authors": [
    {
      "name": "Sunghyeon Jo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0xmb96mh0rxs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04596",
  "fulltext_url": null,
  "id": "f0xmb96mh0rxs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04596",
  "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": "W7211865446",
  "pdf_url": "https://arxiv.org/pdf/2609.04596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0xmb96mh0rxs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Improved Upper Bound for Multicolour Ramsey Numbers",
  "title_text": "An Improved Upper Bound for Multicolour Ramsey Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/f0xmb96mh0rxs",
  "venue": "arXiv",
  "versions": []
}