{"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. Let $H=(V,E)$ be a hypergraph with vertex set $V$ and edge set $E$. $A\\subseteq E$ is a feedback"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10456","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}