{"paper":{"title":"On the boundedness of degenerate hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caihong Yang, Caiyun Hu, Heng Li, Jianfeng Hou, Xizhi Liu, Yixiao Zhang","submitted_at":"2024-06-29T12:37:20Z","abstract_excerpt":"We investigate the impact of a high-degree vertex in Tur\\'{a}n problems for degenerate hypergraphs (including graphs). We say an $r$-graph $F$ is bounded if there exist constants $\\alpha, \\beta>0$ such that for large $n$, every $n$-vertex $F$-free $r$-graph with a vertex of degree at least $\\alpha \\binom{n-1}{r-1}$ has fewer than $(1-\\beta) \\cdot \\mathrm{ex}(n,F)$ edges. The boundedness property is crucial for recent works~\\cite{HHLLYZ23a,DHLY24} that aim to extend the classical Hajnal--Szemer\\'{e}di Theorem and the anti-Ramsey theorems of Erd\\H{o}s--Simonovits--S\\'{o}s.\n  We show that many we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.00427","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/2407.00427/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"}