{
  "abstract": "For a bipartite graph $H$, let $\\operatorname{br}_3(H)$ be the least integer $N$ such that every three-colouring of $K_{N,N}$ contains a monochromatic copy of $H$. We prove that $\\operatorname{br}_3(C_{2n})=3n$ for all sufficiently large $n$, and give the lower bound for every $n\\ge2$. For the upper bound, we reduce a counterexample to a finite rational weighted profile. Cycle extension and vertex-cover arguments force the critical components to have six unique minimum covers which partition the profile. The remaining component supports give a contradiction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29813",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiangdong Ai"
    },
    {
      "name": "Yihan Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dahnmcvwtw9p3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29813",
  "fulltext_url": null,
  "id": "dahnmcvwtw9p3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29813",
  "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": "W7223237698",
  "pdf_url": "https://arxiv.org/pdf/2610.29813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dahnmcvwtw9p3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The three-colour bipartite Ramsey number of sufficiently long even cycles",
  "title_text": "The three-colour bipartite Ramsey number of sufficiently long even cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dahnmcvwtw9p3",
  "venue": "arXiv",
  "versions": []
}