{"paper":{"title":"$H$-free subgraphs of dense graphs maximizing the number of cliques and their blow-ups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Clara Shikhelman, Noga Alon","submitted_at":"2017-06-18T13:01:12Z","abstract_excerpt":"We consider the structure of $H$-free subgraphs of graphs with high minimal degree. We prove that for every $k>m$ there exists an $\\epsilon:=\\epsilon(k,m)>0$ so that the following holds. For every graph $H$ with chromatic number $k$ from which one can delete an edge and reduce the chromatic number, and for every graph $G$ on $n>n_0(H)$ vertices in which all degrees are at least $(1-\\epsilon)n$, any subgraph of $G$ which is $H$-free and contains the maximum number of copies of the complete graph $K_m$ is $(k-1)$-colorable.\n  We also consider several extensions for the case of a general forbidde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05642","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":""},"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"}