{"paper":{"title":"The inducibility of 6-vertex graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jared Le\\'on, Jun Gao, Levente Bodn\\'ar, Oleg Pikhurko, Shumin Sun, Xizhi Liu","submitted_at":"2026-05-29T19:22:36Z","abstract_excerpt":"The inducibility constant $\\lambda_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the case when $F$ has 6 vertices (and there are 78 cases to consider up to isomorphism and complementation). We show that flag algebras can compute the sharp upper bound on $\\lambda_F$ in 36 cases of which, as far as the authors know, 30 are new results. In each of the solved cases, we also prove results about the structure of large (almost) extremal graphs. In particular, we establish perfect stability in all 32 cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00290","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/2606.00290/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"}