{
  "abstract": "The Ramsey number $R(G_1,G_2)$ is the smallest positive integer $n$ such that for every graph $H$ on $n$ vertices, either $H$ contains a copy of $G_1$ or the complement $\\overline H$ contains a copy of $G_2$. Ramsey numbers involving the book graphs $B_n$, which consist of $n$ triangles sharing a common edge, have attracted recent attention, especially in the ``nearly diagonal'' case $R(B_{n-1},B_n)$. Rousseau and Sheehan showed the upper bound $R(B_{n-1},B_n) \\le 4n-1$ nearly fifty years ago, but no general matching lower bound construction is known. This paper gives several new infinite families of $n$ for which $R(B_{n-1},B_n) = 4n-1$. Some of the main results in this paper were found with assistance from the Station, a multi-agent AI system. These results also appeared in a larger work on autonomous mathematical discovery by the authors and Du in arxiv:2608.23691. This paper is a follow-up to that work: we give complete proofs of the book Ramsey results and discuss their connections to objects in combinatorial design theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36522",
  "author_total": 2,
  "authors": [
    {
      "name": "Stephen Chung"
    },
    {
      "name": "William J. Wesley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbkedah90tshb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36522",
  "fulltext_url": null,
  "id": "fbkedah90tshb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36522",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7224122297",
  "pdf_url": "https://arxiv.org/pdf/2610.36522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbkedah90tshb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36522"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Constructions for Nearly Diagonal Book Ramsey Numbers",
  "title_text": "Constructions for Nearly Diagonal Book Ramsey Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fbkedah90tshb",
  "venue": "arXiv",
  "versions": []
}