{"paper":{"title":"Induced Tur\\'an numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Michael Tait, Po-Shen Loh, Rodrigo Zhou","submitted_at":"2016-10-20T17:56:29Z","abstract_excerpt":"The classical K\\H{o}v\\'ari-S\\'os-Tur\\'an theorem states that if $G$ is an $n$-vertex graph with no copy of $K_{s,t}$ as a subgraph, then the number of edges in $G$ is at most $O(n^{2-1/s})$. We prove that if one forbids $K_{s,t}$ as an induced/ subgraph, and also forbids any/ fixed graph $H$ as a (not necessarily induced) subgraph, the same asymptotic upper bound still holds, with different constant factors. This introduces a nontrivial angle from which to generalize Tur\\'an theory to induced forbidden subgraphs, which this paper explores. Along the way, we derive a nontrivial upper bound on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06521","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}