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This confirms a conjecture of R\\\"odl, Ruci\\'nski and Szemer\\'edi, who proved that the minimum $(k-1)$-degree $n/k+O(\\log n)$ suffices. More generally, we show that $H$ contains a matching of size $d$ if its minimum codegree is $d<n/k$, which is also best possible."},"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":"1404.1136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-04T02:49:01Z","cross_cats_sorted":[],"title_canon_sha256":"2fbb93dcb3008199bb31e52ce5ae676be2c260da49aac33b610467782a9cc216","abstract_canon_sha256":"7341e427fab54aab5daac824a213cbe42c3349d4156616d1c1d5587554c14f59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:56.164916Z","signature_b64":"q4BcnwXELXq02Cg8Uu0v/807E2lJoqZNkzMIUNdmx5mWvXgpvTEO3hKFi+cl5ZIcsoLlL0MuVJ1lAEl3WTAVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52f2b57d6ebcdeadde7300d45a950f961a41f7173d34926d9cb8162d523c5908","last_reissued_at":"2026-05-18T02:40:56.164478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:56.164478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Near Perfect Matchings in $k$-uniform Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han","submitted_at":"2014-04-04T02:49:01Z","abstract_excerpt":"Let $H$ be a $k$-uniform hypergraph on $n$ vertices where $n$ is a sufficiently large integer not divisible by $k$. 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