{"paper":{"title":"Multicut is FPT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jean Daligault, Nicolas Bousquet, St\\'ephan Thomass\\'e","submitted_at":"2010-10-25T17:18:00Z","abstract_excerpt":"Let $G=(V,E)$ be a graph on $n$ vertices and $R$ be a set of pairs of vertices in $V$ called \\emph{requests}. A \\emph{multicut} is a subset $F$ of $E$ such that every request $xy$ of $R$ is cut by $F$, \\i.e. every $xy$-path of $G$ intersects $F$. We show that there exists an $O(f(k)n^c)$ algorithm which decides if there exists a multicut of size at most $k$. In other words, the \\M{} problem parameterized by the solution size $k$ is Fixed-Parameter Tractable. The proof extends to vertex multicuts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5197","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"}