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Except for a few special cases, this conjecture remains wide open. However, it is known that a H-free graph must contain a complete or empty bipartite graph with parts of polynomial size. We prove an analogue of this result for 3-uniform hypergraphs, showing that if a 3-uniform hypergraph on n vertices is H-free, for any given H, then i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.5544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-29T02:55:11Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ef1551c4a99023e32aa049ae063bb4d06bc1736a47a4721e0a54ebf6cdaf130c","abstract_canon_sha256":"519331729a1bed177047090bbf998f8fefdd157b78d84c2f4734150aa91f2651"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:20.808591Z","signature_b64":"Q+oCEiK6eQMDUBXU0rlyHaqHUxINXc3/ke2V2BAAfoRJnLRsDww8cV8rmoF3nMl0++W/D1mm7cgf893guW0RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c97dbc7fe603e1dacea52982ac9802c657fae9742fdcbab995380cb7d96856b","last_reissued_at":"2026-05-18T04:23:20.808038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:20.808038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erdos-Hajnal-type theorems in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Benny Sudakov, David Conlon, Jacob Fox","submitted_at":"2011-04-29T02:55:11Z","abstract_excerpt":"The Erdos-Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not contain an induced copy of a given graph H, then it must contain either a clique or an independent set of size n^{d(H)}, where d(H) > 0 depends only on the graph H. 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