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Motivated by a classic result in graph theory that every $n$-vertex cycle-free graph has at most $n-1$ edges, S\\'os and, independently, Verstra\\\"ete asked whether for every integer $k$, a $k$-uniform $n$-vertex hypergraph without any tight $k$-uniform cycles has at most $\\binom{n-1}{k-1}$ edges. In this paper, we answer this question in negative."},"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":"1711.07442","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T17:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"796502769a6716685359396b6d934d6dee8a7fbe066880c1db10c5ec9c5728ec","abstract_canon_sha256":"b85ff990a4cf77fa12e7064a2bd1548b70135bdb81d103065903fa3ebb1a1521"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:10.227712Z","signature_b64":"RnvVA2qs+U17hv6D6lt5Zg3944S0uJAJqow+TIXxPGOezQ4obuyD9VB42gzQYDincjEoZJB+XYgA64KonH33Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dabd577eeec1bdeb7cc6221df625cc069d0881de6f8ccd4b6feb5e85ef837c21","last_reissued_at":"2026-05-18T00:28:10.227042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:10.227042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On tight cycles in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Huang, Jie Ma","submitted_at":"2017-11-20T17:57:46Z","abstract_excerpt":"A tight $k$-uniform $\\ell$-cycle, denoted by $TC_\\ell^k$, is a $k$-uniform hypergraph whose vertex set is $v_0, \\cdots, v_{\\ell-1}$, and the edges are all the $k$-tuples $\\{v_i, v_{i+1}, \\cdots, v_{i+k-1}\\}$, with subscripts modulo $\\ell$. Motivated by a classic result in graph theory that every $n$-vertex cycle-free graph has at most $n-1$ edges, S\\'os and, independently, Verstra\\\"ete asked whether for every integer $k$, a $k$-uniform $n$-vertex hypergraph without any tight $k$-uniform cycles has at most $\\binom{n-1}{k-1}$ edges. 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