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For nontrivial 3-uniform hypergraphs $H$, the function $r_k(H)$ ranges from $\\sqrt{6k}(1+o(1))$ to double exponential in $k$.\n  We observe that $r_k(H)$ is polynomial in $k$ when $H$ is $r$-partite and at least single-exponential in $k$ otherwise. Erd\\H{o}s, Hajnal and Rado gave bounds for large cliques $K_s^r$ with $s\\ge "},"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":"1302.5304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-21T15:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"d0bba9cefac2c428da612e8cf49fd6077dc3af85ae258fc2b3ffdf51502da6ac","abstract_canon_sha256":"d2f0b0217f656430a50db618d851243711046db734cfc9df41d8e9963a32d92e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:58.079094Z","signature_b64":"iB2RpGDgbkOm4ykFoxYNOoB8oWxMWUeO/JlaA/majxIXFivwvBLhxhNQQoPKkGJZkHFg16j/X6IXOYjZQm7RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13bdb176b31308ad384f812dc8ab2759de7af9c7ed7b3f3b5dad82373f00626a","last_reissued_at":"2026-05-18T03:32:58.078425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:58.078425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multicolor Ramsey numbers for triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andras Gyarfas, Dhruv Mubayi, Hong Liu, Maria Axenovich","submitted_at":"2013-02-21T15:28:31Z","abstract_excerpt":"Given an $r$-uniform hypergraph $H$, the multicolor Ramsey number $r_k(H)$ is the minimum $n$ such that every $k$-coloring of the edges of the complete $r$-uniform hypergraph $K_n^r$ yields a monochromatic copy of $H$. We investigate $r_k(H)$ when $k$ grows and $H$ is fixed. For nontrivial 3-uniform hypergraphs $H$, the function $r_k(H)$ ranges from $\\sqrt{6k}(1+o(1))$ to double exponential in $k$.\n  We observe that $r_k(H)$ is polynomial in $k$ when $H$ is $r$-partite and at least single-exponential in $k$ otherwise. 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