{
  "abstract": "For a fixed graph $T$ and a fixed nonempty family $\\mathcal{F}$ of graphs, let $\\operatorname{ex}(G, T, \\mathcal{F})$ denote the maximum number of copies of $T$ in an $\\mathcal{F}$-free subgraph of a graph $G$. Alon and Shikhelman~[Algorithmica, 2022] conjectured that if $e(T)> 0$ and no member of $\\mathcal{F}$ is a subgraph of a blow-up of $T$, then for every $\\varepsilon>0$, approximating $\\operatorname{ex}(G, T, \\mathcal{F})$ within an additive error $n^{v(T)-\\varepsilon}$ is NP-hard for an input graph $G$ on $n$ vertices. The previously established general cases for this conjecture include $\\operatorname{ex}(G, K_2, \\mathcal{F})$ by Alon, Shapira and Sudakov~[Ann. of Math., 2009], and $\\operatorname{ex}(G, K_m, K_k)$ by Alon and Shikhelman. In this paper, we confirm this conjecture for every bipartite graph $T$ and every clique $T$. Our reductions use iterative leaf additions, symmetric rooted extensions and random transversals to encode the maximum number of edges in a $(k-1)$-colorable subgraph of $G$, where $k=\\min_{F\\in \\mathcal{F}}χ(F)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16358",
  "author_total": 5,
  "authors": [
    {
      "name": "Yihan Chen"
    },
    {
      "name": "Jialin He"
    },
    {
      "name": "Xihe Li"
    },
    {
      "name": "Jie Ma"
    },
    {
      "name": "Tianying Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3pkkx67mnbds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16358",
  "fulltext_url": null,
  "id": "a3pkkx67mnbds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16358",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221828237",
  "pdf_url": "https://arxiv.org/pdf/2610.16358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3pkkx67mnbds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "NP-hardness of additive approximation for generalized Turán problems",
  "title_text": "NP-hardness of additive approximation for generalized Turán problems",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/a3pkkx67mnbds",
  "venue": "arXiv",
  "versions": []
}