{"paper":{"title":"Generalized Erd\\H{o}s--Rogers problems for $r$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lulu Dai, Qizhong Lin","submitted_at":"2026-07-01T10:17:22Z","abstract_excerpt":"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, if \\(r\\ge3\\), \\(F\\) is nonempty, \\(G\\) is \\(2\\)-tightly connected, and there is no homomorphism from \\(G\\) to \\(F\\), then \\[\n  f_{F,G}(n)\\le C(\\log n)^{\\beta_F},\n  \\qquad\n  \\beta_F=\n  \\max_{\\substack{\\emptyset\\ne P\\subseteq\\partial_2F}}\n  \\frac{e(P)}{v(P)-1}. \\] For \\(r=3\\), this confirms a conjecture of He and Nie for tightly connected \\(3\\)-graphs, sharpening their ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00732","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00732/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}