{
  "abstract": "Let $γ(G)$ denote the number of cliques in a graph $G$ and let $Γ(n):= \\{γ(G):|V(G)|=n\\}$ be the set of values of $γ(G)$ that can be attained on $n$ vertices. We improve on a result by Erdős and Erné to show that $| Γ(n)| \\geq 2^{n-4\\ln(2)\\log^3(n)}$ for sufficiently large $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21739",
  "author_total": 3,
  "authors": [
    {
      "name": "Mihir Neve"
    },
    {
      "name": "Alexey Pokrovskiy"
    },
    {
      "name": "Andrey Shapiro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f5pbefazchwct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21739",
  "fulltext_url": null,
  "id": "f5pbefazchwct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21739",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213919234",
  "pdf_url": "https://arxiv.org/pdf/2609.21739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f5pbefazchwct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21739"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Range of Clique Counts in Graphs",
  "title_text": "Range of Clique Counts in Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/f5pbefazchwct",
  "venue": "arXiv",
  "versions": []
}