{"paper":{"title":"Strong Forms of Stability from Flag Algebra Calculations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jakub Sliacan, Konstantinos Tyros, Oleg Pikhurko","submitted_at":"2017-06-08T14:36:16Z","abstract_excerpt":"Given a hereditary family $\\mathcal{G}$ of admissible graphs and a function $\\lambda(G)$ that linearly depends on the statistics of order-$\\kappa$ subgraphs in a graph $G$, we consider the extremal problem of determining $\\lambda(n,\\mathcal{G})$, the maximum of $\\lambda(G)$ over all admissible graphs $G$ of order $n$. We call the problem perfectly $B$-stable for a graph $B$ if there is a constant $C$ such that every admissible graph $G$ of order $n\\ge C$ can be made into a blow-up of $B$ by changing at most $C(\\lambda(n,\\mathcal{G})-\\lambda(G)){n\\choose2}$ adjacencies. As special cases, this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02612","kind":"arxiv","version":2},"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"}