{
  "abstract": "For graphs $F$, $G$, and $H$, we write $F \\to (G, H)$ if every red/blue edge-coloring of $F$ contains either a red copy of $G$ or a blue copy of $H$. The Ramsey number $R(G, H)$ is the smallest integer $N$ such that $K_N \\to (G, H)$. Let $H := K_k + nK_h$ be the generalized book graph, and let $G := K_{p+1}(a_1, a_2, \\dots, a_{p+1})$ be a complete $(p+1)$-partite graph satisfying $a_1 = 1$, $a_2 \\mid (nh-1)$, and $a_i \\le a_{i+1}$. In this paper, avoiding the use of Szemerédi's regularity lemma, we prove that for any fixed $h, p \\ge 1$, $k \\ge 2$, and sufficiently large $n$, $K_{p(nh + a_2k - 1) + 1} \\setminus K_{1, nh - a_2(h-2) - 1}\\to(G, H).$ This result yields the star-critical Ramsey number $r_*(G, H) = (p-1)(nh + a_2k - 1) + a_2(k + h - 2) + 1.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11151",
  "author_total": 3,
  "authors": [
    {
      "name": "Peiyu Huang"
    },
    {
      "name": "Qizhong Lin"
    },
    {
      "name": "Lin Niu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5387gn6fjrfw3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11151",
  "fulltext_url": null,
  "id": "5387gn6fjrfw3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11151",
  "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": "W7221167271",
  "pdf_url": "https://arxiv.org/pdf/2610.11151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5387gn6fjrfw3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.11151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Star-critical Ramsey numbers involving large generalized books",
  "title_text": "Star-critical Ramsey numbers involving large generalized books",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/5387gn6fjrfw3",
  "venue": "arXiv",
  "versions": []
}