{"paper":{"title":"On the Linear Cycle Cover Conjecture of Gy\\'arf\\'as and S\\'ark\\\"ozy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Beka Ergemlidze, Ervin Gy\\H{o}ri","submitted_at":"2016-09-15T18:15:51Z","abstract_excerpt":"A linear cycle in a hypergraph $H$ is a cyclic sequence of hyperedges such that two consecutive hyperedges intersect in exactly one element and two nonconsecutive hyperedges are disjoint and $\\alpha(H)$ denotes the size of a largest independent set of $H$. In this note, we show that the vertex set of every $3$-uniform hypergraph $H$ can be covered by at most $\\alpha(H)$ pairwise edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gy\\'arf\\'as and S\\'ark\\\"ozy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04761","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"}