{
  "abstract": "Let $B_n$ be the book graph consisting of $n$ triangles sharing a common edge. We prove upper bounds for $r(B_{\\lceilαn\\rceil},B_n)$ that asymptotically match the known lower bounds in the remaining range $1/6<α<1/4$. Combined with the known results for the other ranges of $α$, this completely determines the asymptotics of the Ramsey number $r(B_{\\lceilαn\\rceil},B_n)$ for every fixed $0<α\\le1$: \\[ r(B_{\\lceilαn\\rceil},B_n)=(c(α)+o(1))n, \\qquad c(α)= \\begin{cases} 2, & 0<α\\le1/6,\\\\[1mm] \\displaystyle\\frac{3}{1+2p_α^2}, & 1/6<α\\leα_0,\\\\[3mm] (1+\\sqrtα)^2, & α_0<α\\le1, \\end{cases} \\] where \\(α_0:=\\frac{52-16\\sqrt3}{121}, \\;\\; p_α:=\\frac{1-\\sqrt{α(3-2α)}}{1-2α} \\;\\; (1/6<α\\leα_0).\\) Consequently, the random lower bound is asymptotically tight if and only if $α\\geα_0$, thereby determining exactly the range of $α$ for which the conjecture of Conlon, Fox and Wigderson holds. The proof develops a defect-compensation framework around a $K_4$-free auxiliary graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38515",
  "author_total": 3,
  "authors": [
    {
      "name": "Lulu Dai"
    },
    {
      "name": "Chunchao Fan"
    },
    {
      "name": "Qizhong Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yecefwffp921.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38515",
  "fulltext_url": null,
  "id": "3yecefwffp921",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38515",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38515",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yecefwffp921.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38515",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38515"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The asymptotics of off-diagonal book Ramsey numbers",
  "title_text": "The asymptotics of off-diagonal book Ramsey numbers",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3yecefwffp921",
  "venue": "arXiv",
  "versions": []
}