{
  "abstract": "The Turán number $\\rm ex(n,H)$ of a given graph $H$ is the maximum number of edges in an $n$-vertex $H$-free graph. In this paper, for all $p\\ge q\\ge r\\ge 2$ and $n\\geq p+q+r$, we determine the exact value of $\\rm ex(n,K_p\\cup K_q\\cup K_r)$ and describe all extremal graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38430",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexandr Kostochka"
    },
    {
      "name": "Dadong Peng"
    },
    {
      "name": "Zimu Xiang"
    },
    {
      "name": "Liang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hfzg9cha7qyr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38430",
  "fulltext_url": null,
  "id": "2hfzg9cha7qyr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38430",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hfzg9cha7qyr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38430"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Turán number of three disjoint cliques of arbitrary sizes",
  "title_text": "Turán number of three disjoint cliques of arbitrary sizes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2hfzg9cha7qyr",
  "venue": "arXiv",
  "versions": []
}