{
  "abstract": "Let $B_k$ denote the book consisting of $k$ triangles sharing a common edge. We prove that there exist absolute constants $ρ>0$ and $N$ such that, for every pair of integers $n,k$ with $n\\ge N$ and $2\\le k\\le ρn$, writing $n=5q+r$ with $0\\le r<5$, \\[ \\operatorname{ex}(n,C_5,B_k)=q^{\\,5-r}(q+1)^r, \\] with the balanced complete $C_5$-blow-ups as the only extremal graphs. The linear order of this range is best possible since for all sufficiently large $n$, the formula fails whenever $k\\ge0.14n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06753",
  "author_total": 1,
  "authors": [
    {
      "name": "Wentao Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezf34bgvyczpe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06753",
  "fulltext_url": null,
  "id": "ezf34bgvyczpe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06753",
  "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/2611.06753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezf34bgvyczpe.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Exact Number of Pentagons in Book-Free Graphs",
  "title_text": "The Exact Number of Pentagons in Book-Free Graphs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/ezf34bgvyczpe",
  "venue": "arXiv",
  "versions": []
}