{"paper":{"title":"Close relatives (of Feedback Vertex Set), revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Hugo Jacob, Marcin Pilipczuk, Oscar Defrain, Thomas Bellitto","submitted_at":"2021-06-30T12:30:32Z","abstract_excerpt":"At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k \\log k)} \\cdot n^{\\mathcal{O}(1)}$-time algorithm on graphs of treewidth at most $k$, assuming the Exponential Time Hypothesis. This contrasts with the $3^{k} \\cdot k^{\\mathcal{O}(1)} \\cdot n$-time algorithm for FVS using the Cut&Count technique.\n  During their live talk at IPEC 2020, Bergougnoux et al.~posed a number of open questions, which we answer in this work.\n  - Subset Even Cycle Transversal, Subset Odd Cycle Transversal,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.16015","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/2106.16015/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"}