{
  "abstract": "Let $X^{(r)}_n$ denote the number of copies of a complete graph $K_r$ in the random intersection graph model on $n$ vertices. We derive upper bounds on the distance between the standardized version of $X^{(r)}_n$ and the standard normal distribution, measured in both the Kolmogorov and Wasserstein metrics. We complement these results with necessary and sufficient conditions for asymptotic normality. As a byproduct, we provide precise estimates for the variance of $X^{(r)}_n$. In the process, we develop new general techniques for analysing so--called clique covers, which play a crucial role in the study of subgraph probabilities in random intersection graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27128",
  "author_total": 2,
  "authors": [
    {
      "name": "Katarzyna Rybarczyk"
    },
    {
      "name": "Grzegorz Serafin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wqmbn446bdqd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27128",
  "fulltext_url": null,
  "id": "9wqmbn446bdqd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27128",
  "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": "W7223136288",
  "pdf_url": "https://arxiv.org/pdf/2610.27128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wqmbn446bdqd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Normal approximation for subgraph counts in random intersection graphs: the case of cliques",
  "title_text": "Normal approximation for subgraph counts in random intersection graphs: the case of cliques",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9wqmbn446bdqd",
  "venue": "arXiv",
  "versions": []
}