{
  "abstract": "An $n$-vertex graph $G$ is $(ρ, d)$-dense if for all $U \\subseteq V(G)$ of size at least $ρn$, the induced subgraph $G[U]$ contains at least $\\frac{d}{2}|U|^2$ edges. In 2010, partly motivated by the theory of quasirandomness, Kohayakawa, Nagle, Rödl, and Schacht conjectured that, for any fixed graph $F$, the number of homomorphic copies of $F$ in a given $n$-vertex $(o(1),d)$-dense graph is at least $(1-o(1))d^{e(F)}n^{v(F)}$. Despite considerable effort, only a few graphs are known to satisfy the conjecture. We find a new broad class of graphs that satisfy the conjecture, including cographs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13820",
  "author_total": 1,
  "authors": [
    {
      "name": "Hyunwoo Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amezp2vxr4xz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13820",
  "fulltext_url": null,
  "id": "amezp2vxr4xz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13820",
  "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": "W7221505124",
  "pdf_url": "https://arxiv.org/pdf/2610.13820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amezp2vxr4xz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting cographs in locally dense graphs",
  "title_text": "Counting cographs in locally dense graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/amezp2vxr4xz5",
  "venue": "arXiv",
  "versions": []
}