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Recently, DeMarco and Kahn proved this for $p > K \\sqrt{\\log n/n}$ for some constant $K$, and apart from the value of the constant this bound is best possible. We study an extremal problem of this type in random hypergraphs. Denote by $F_5$, which sometimes called as the generalized triangle, the 3-uniform hyper"},"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":"1310.1501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-05T17:56:17Z","cross_cats_sorted":[],"title_canon_sha256":"610c12d29c0f6cc6f1efdf3e843c273b133e5453abb9b9ad0fc06ab9b89d5e4f","abstract_canon_sha256":"a22b96814cbc8616b36a7621cc4d80cd0b0ca59643d1c25f61824eabff932b77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:59.195755Z","signature_b64":"zX6Mea6Dt7/28N8i2ol9xHTFXC3iWDeGPB90ICHTjXxjXCXk8EyC2MjYWkpBgLyKqgiN3ZwM1xco026ghIeVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee77736d17e7956db136b3c85a88830c11d6b3b18818138575922cddfecdfe91","last_reissued_at":"2026-05-18T02:00:59.195271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:59.195271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mantel's Theorem for Random Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jane Butterfield, John Lenz, J\\'ozsef Balogh, Ping Hu","submitted_at":"2013-10-05T17:56:17Z","abstract_excerpt":"A classical result in extremal graph theory is Mantel's Theorem, which states that every maximum triangle-free subgraph of $K_n$ is bipartite. 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