{"paper":{"title":"Long cycles have the edge-Erd\\H{o}s-P\\'osa property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Joos, Henning Bruhn, Matthias Heinlein","submitted_at":"2016-07-07T07:51:12Z","abstract_excerpt":"We prove that the set of long cycles has the edge-Erd\\H{o}s-P\\'osa property: for every fixed integer $\\ell\\ge 3$ and every $k\\in\\mathbb{N}$, every graph $G$ either contains $k$ edge-disjoint cycles of length at least $\\ell$ (long cycles) or an edge set $X$ of size $O(k^2\\log k + \\ell k)$ such that $G-X$ does not contain any long cycle. This answers a question of Birmel\\'e, Bondy, and Reed (Combinatorica 27 (2007), 135--145)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01903","kind":"arxiv","version":3},"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"}