{
  "abstract": "For graphs $G, T$ and a graph-family $\\mathcal{H}$, let $ex(G,T,\\mathcal{H})$ denote the maximum possible number of copies of $T$ in an $\\mathcal{H}$-free subgraph of $G$. Alon and Shikhelman conjectured that for every family of graphs $\\mathcal{H}$ with $χ(H) > s$ for every $H \\in \\mathcal{H}$, it is NP-hard to compute $ex(G,K_s,\\mathcal{H})$, and even to approximate it up to additive error $n^{s-δ}$ on $n$-vertex graphs, for any fixed $δ> 0$. The case $s=2$ was established in a breakthrough result of Alon, Shapira and Sudakov. We prove the Alon-Shikhelman conjecture for finite families $\\mathcal{H}$. In particular, we obtain an elementary proof of the Alon-Shapira-Sudakov result when $\\mathcal{H}$ is finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30654",
  "author_total": 3,
  "authors": [
    {
      "name": "Lior Gishboliner"
    },
    {
      "name": "Yevgeny Levanzov"
    },
    {
      "name": "Asaf Shapira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1yb3gx6j9fbzf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30654",
  "fulltext_url": null,
  "id": "1yb3gx6j9fbzf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30654",
  "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": "W7223308055",
  "pdf_url": "https://arxiv.org/pdf/2610.30654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1yb3gx6j9fbzf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30654"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "NP-Hardness of Generalized-Turán Graph Modification Problems",
  "title_text": "NP-Hardness of Generalized-Turán Graph Modification Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1yb3gx6j9fbzf",
  "venue": "arXiv",
  "versions": []
}