{
  "abstract": "Let \\(B_n\\) denote the book graph consisting of \\(n\\) triangles sharing a common edge. Rousseau and Sheehan (1978) proved, using Paley graphs, that \\(R(B_n,B_n)=4n+2\\) whenever \\(4n+1\\) is a prime power. Since then, only a few additional exact values of \\(R(B_n,B_n)\\) have been obtained. In this paper, we obtain \\(R(B_n,B_n)=4n+1\\) for infinitely many \\(n\\) by constructing graphs from pseudo-cyclic strongly regular graphs (PC-graphs). To the best of our knowledge, this is the first new infinite family of exact diagonal book Ramsey numbers since 1978. We also prove that \\(R(B_{n-2},B_n)\\le 4n-3\\) for every \\(n\\ge 3\\) with \\(n\\ne 6\\), removing the original condition \\(n\\equiv 2\\pmod 3\\) imposed by Rousseau and Sheehan. Moreover, equality \\(R(B_{n-2},B_n)=4n-3\\) holds if there exists a symmetric Hadamard matrix of order \\(2n-2\\) with all diagonal entries equal to \\(1\\). In particular, this equality holds for every \\(n=2^{2\\ell-1}+1\\) with \\(\\ell\\ge 1\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.07214",
  "author_total": 2,
  "authors": [
    {
      "name": "Lulu Dai"
    },
    {
      "name": "Qizhong Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pnwznr57v0xm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.07214",
  "fulltext_url": null,
  "id": "4pnwznr57v0xm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.07214",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7163887635",
  "pdf_url": "https://arxiv.org/pdf/2606.07214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pnwznr57v0xm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2606.07214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.07214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Book Ramsey numbers via algebraic constructions",
  "title_text": "Book Ramsey numbers via algebraic constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4pnwznr57v0xm",
  "venue": "arXiv",
  "versions": []
}