{"paper":{"title":"On the Erd\\H{o}s-Hajnal conjecture for six-vertex tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eli Berger, Krzysztof Choromanski, Maria Chudnovsky","submitted_at":"2015-08-20T14:12:26Z","abstract_excerpt":"A celebrated unresolved conjecture of Erd\\H{o}s and Hajnal states that for every undirected graph $H$ there exists $\\epsilon(H)>0$ such that every undirected graph on $n$ vertices that does not contain $H$ as an induced subgraph contains a clique or stable set of size at least $n^{\\epsilon(H)}$. The conjecture has a directed equivalent version stating that for every tournament $H$ there exists $\\epsilon(H)>0$ such that every $H$-free $n$-vertex tournament $T$ contains a transitive subtournament of order at least $n^{\\epsilon(H)}$. We say that a tournament is \\textit{prime} if it does not have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04992","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"}