{"paper":{"title":"On Feedback Vertex Set: New Measure and New Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jianer Chen, Yang Liu, Yixin Cao","submitted_at":"2010-04-10T03:05:53Z","abstract_excerpt":"We present a new parameterized algorithm for the {feedback vertex set} problem ({\\sc fvs}) on undirected graphs. We approach the problem by considering a variation of it, the {disjoint feedback vertex set} problem ({\\sc disjoint-fvs}), which finds a feedback vertex set of size $k$ that has no overlap with a given feedback vertex set $F$ of the graph $G$. We develop an improved kernelization algorithm for {\\sc disjoint-fvs} and show that {\\sc disjoint-fvs} can be solved in polynomial time when all vertices in $G \\setminus F$ have degrees upper bounded by three. We then propose a new branch-and-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1672","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":""},"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"}