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This result can be viewed as a special case of the degree version of a well-known conjecture of Erd\\H{o}s on hypergraph matchings. Improving the work of Bollob\\'as, Daykin, and Erd\\H os from 1976, we show that given integers $n, k, s$ with $n\\ge 3k^2 s$, every $k$-uniform hypergraph $H$ on $n$ vertices with minimum vertex degree greater than $\\binom{n-1}{k-1}-"},"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":"1605.07535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-24T16:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"d522e29d3e41063e001eed0cf2cd5d0e7ab99b3822daa46a63b7d6448c1c4817","abstract_canon_sha256":"1dab055a9cb391807597be96d1d83b2948db2d84994a6b671dec15eaf6a18b72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:45.797045Z","signature_b64":"qAoQFk4I8LrU1xrBoL6AaNdT+Cp7HFb1y90SmkyRqH6NZZPOhtWqoBAtTJcdZW/1gf/UmPCCbvKVw4p2pbEYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef36ae52fd43c530227fac7bdf3d43e51d4f850cffa0fa9deed3274f70883add","last_reissued_at":"2026-05-18T01:13:45.796456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:45.796456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Huang, Yi Zhao","submitted_at":"2016-05-24T16:32:09Z","abstract_excerpt":"We use an algebraic method to prove a degree version of the celebrated Erd\\H os-Ko-Rado theorem: given $n>2k$, every intersecting $k$-uniform hypergraph $H$ on $n$ vertices contains a vertex that lies on at most $\\binom{n-2}{k-2}$ edges. 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