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We define a class of $(\\e,p)$-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type $\\ell$ Hamilton cycles, where $\\ell<k/2$."},"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":"1102.1488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-08T01:48:52Z","cross_cats_sorted":[],"title_canon_sha256":"430c43221883a3173d2a52db85c28d667292c7c2a766d23b136cd464cc609557","abstract_canon_sha256":"ae58b419aeb502418d44c222e5a056e4ec15b60175ab83b7dc697a2fc10b6e1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:53.130361Z","signature_b64":"TSjy/KOIAKl7zDn/2feprR/BzLlgghkgq0i5LsH7BOOhaNtB0Cv5FS0tdKloC0qxAs95YPeO1HXi+d185QXkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f95316caf531861a97ba2107d6f23e1f4aa1b1907fc653c8942dd0e091e9fbf","last_reissued_at":"2026-05-18T04:29:53.129877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:53.129877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing tight Hamilton cycles in uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Deepak Bal","submitted_at":"2011-02-08T01:48:52Z","abstract_excerpt":"We say that a $k$-uniform hypergraph $C$ is a Hamilton cycle of type $\\ell$, for some $1\\le \\ell \\le k$, if there exists a cyclic ordering of the vertices of $C$ such that every edge consists of $k$ consecutive vertices and for every pair of consecutive edges $E_{i-1},E_i$ in $C$ (in the natural ordering of the edges) we have $|E_{i-1}\\setminus E_i|=\\ell$. 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