{
  "abstract": "Let \\(F\\) and \\(G\\) be \\(r\\)-uniform hypergraphs, and let \\(f_{F,G}(n)\\) be the largest integer \\(m\\) such that every \\(n\\)-vertex \\(G\\)-free \\(r\\)-graph contains an induced \\(F\\)-free subgraph on \\(m\\) vertices. We prove that, for \\(r\\ge3\\) and \\(2\\le k\\le r-1\\), if \\(F\\) is nonempty, \\(G\\) is \\(k\\)-tightly connected, and there is no homomorphism from \\(G\\) to \\(F\\) (that is, \\(G\\not\\to F\\)), then \\[ f_{F,G}(n)\\le C(\\log n)^{β_F^{(k)}}, \\qquad β_F^{(k)}= \\max_{\\emptyset\\ne P\\subseteq\\partial_kF} \\frac{e(P)}{v(P)-1}. \\] The case \\(r=3\\) of our result resolves a conjecture of He and Nie. As a consequence, we obtain the Ramsey lower bound \\(r(G,K_n^r)\\ge2^{Ω\\bigl(n^{(r-1)/\\binom rk}\\bigr)}\\) for every \\(k\\)-tightly connected non-\\(r\\)-partite \\(r\\)-graph \\(G\\). This extends a result of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstraëte and Yu from the \\(3\\)-uniform setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.00732",
  "author_total": 2,
  "authors": [
    {
      "name": "Lulu Dai"
    },
    {
      "name": "Qizhong Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c03ea4pw1q7m2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.00732",
  "fulltext_url": null,
  "id": "c03ea4pw1q7m2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.00732",
  "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": "W7167073504",
  "pdf_url": "https://arxiv.org/pdf/2607.00732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c03ea4pw1q7m2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2607.00732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.00732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tight connectivity and shadow densities in generalized Erdős--Rogers problems",
  "title_text": "Tight connectivity and shadow densities in generalized Erdős--Rogers problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/c03ea4pw1q7m2",
  "venue": "arXiv",
  "versions": []
}