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In this paper, we prove $(i)$ if $H$ is a linear $3$-uniform hypergraph with $m$ edges, then $\\tau_c(H)\\le m/3$. $(ii)$ if $H$ is a $3$-uniform hypergraph with $m$ edges, then $\\tau_c(H)\\le m/2$ and furthermore, the equality holds on if and only if every component of $H$ is a $2-$cycle. Let $H=(V,E)$ be a hypergraph with vertex set $V$ and edge set $E$. $A\\subseteq E$ is a feedback"},"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":"1807.10456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-27T06:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"6d65a61e9c22eaf8711850a27834d3b4a21f0ee6c56ce46c1647c5c443a93606","abstract_canon_sha256":"cf3bcfc9e6074d1edd767f0b2e10696807fa54f256c1bb8a5ced2b8b29564dea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:40.541730Z","signature_b64":"klv2iNTi8SkkVZeETq1Xd/nlj0VIOhzNx5VtjCaBVHJfhpRj0TYfBhHD5m1jP5GjR5Hs0jdLv4NcnYreoHeJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f62368d120c513d4f430d6468e9ce2ce72350952366c9f5cd3fe0cdd6ffa090","last_reissued_at":"2026-05-18T00:09:40.540866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:40.540866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the feedback number of 3-uniform hypergraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhongzheng Tang, Zhuo Diao","submitted_at":"2018-07-27T06:51:52Z","abstract_excerpt":"Let $H=(V,E)$ be a hypergraph with vertex set $V$ and edge set $E$. $S\\subseteq V$ is a feedback vertex set (FVS) of $H$ if $H\\setminus S$ has no cycle and $\\tau_c(H)$ denote the minimum cardinality of a FVS of $H$. In this paper, we prove $(i)$ if $H$ is a linear $3$-uniform hypergraph with $m$ edges, then $\\tau_c(H)\\le m/3$. $(ii)$ if $H$ is a $3$-uniform hypergraph with $m$ edges, then $\\tau_c(H)\\le m/2$ and furthermore, the equality holds on if and only if every component of $H$ is a $2-$cycle. 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