{"paper":{"title":"Towards a conjecture of Birmel\\'e-Bondy-Reed on the Erd\\H{o}s-P\\'osa property of long cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunlei Zu, Jie Ma","submitted_at":"2021-12-28T09:27:14Z","abstract_excerpt":"A conjecture of Birmel\\'e, Bondy and Reed states that for any integer $\\ell\\geq 3$, every graph $G$ without two vertex-disjoint cycles of length at least $\\ell$ contains a set of at most $\\ell$ vertices which meets all cycles of length at least $\\ell$. They showed the existence of such a set of at most $2\\ell+3$ vertices. This was improved by Meierling, Rautenbach and Sasse to $5\\ell/3+29/2$. Here we present a proof showing that at most $3\\ell/2+7/2$ vertices suffice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.14065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}