{"paper":{"title":"A coarse Erd\\H{o}s-P\\'{o}sa theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. Pascal Gollin, Jungho Ahn, O-joung Kwon, Tony Huynh","submitted_at":"2024-07-08T12:44:18Z","abstract_excerpt":"An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic Erd\\H{o}s-P\\'osa theorem to induced packings of cycles. More specifically, we show that there exist functions $f(k,\\ell)=\\mathcal{O}(\\ell k\\log k)$ and $g(k)=\\mathcal{O}(k\\log k)$ such that for all integers $k\\geq1$ and $\\ell\\geq3$, every graph $G$ contains either an induced packing of $k$ cycles of length at least $\\ell$, not necessarily induced cycles, or sets $X_1$ and $X_2$ of vertices with $|X_1|\\leq f(k,\\ell)$ and $|X_2|\\leq g(k)$ such that, after removing the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05883","kind":"arxiv","version":2},"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/2407.05883/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"}