{
  "abstract": "For a graph \\(G\\), let \\(\\operatorname{cp}(G)\\) and \\(\\operatorname{cc}(G)\\) be the minimum numbers of cliques in an edge partition and a clique cover of \\(G\\), respectively. Set $σ_n = \\max_{\\lvert V(G)\\rvert=n} \\bigl(\\operatorname{cp}(G)-\\operatorname{cc}(G)\\bigr), d_n=\\left\\lfloor\\frac{n^2}{4}\\right\\rfloor-σ_n.$ In 1983, Erdős, Faudree, and Ordman asked whether \\(d_n=O(n)\\). Caccetta, Erdős, Ordman, and Pullman previously constructed graphs showing \\(d_n=O(n^{3/2})\\). We prove that $d_n=Θ(n^{4/3}),$ thereby determining the correct order of the deficit and answering their question in the negative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20305",
  "author_total": 1,
  "authors": [
    {
      "name": "Bo Ning"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6y0q0aywxek1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20305",
  "fulltext_url": null,
  "id": "a6y0q0aywxek1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20305",
  "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": "W7213599420",
  "pdf_url": "https://arxiv.org/pdf/2609.20305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6y0q0aywxek1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the difference between clique partition and clique covering numbers",
  "title_text": "On the difference between clique partition and clique covering numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/a6y0q0aywxek1",
  "venue": "arXiv",
  "versions": []
}