{"paper":{"title":"Fixed-parameter tractable canonization and isomorphism test for graphs of bounded treewidth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Daniel Lokshtanov, Marcin Pilipczuk, Micha{\\l} Pilipczuk, Saket Saurabh","submitted_at":"2014-04-03T09:49:54Z","abstract_excerpt":"We give a fixed-parameter tractable algorithm that, given a parameter $k$ and two graphs $G_1,G_2$, either concludes that one of these graphs has treewidth at least $k$, or determines whether $G_1$ and $G_2$ are isomorphic. The running time of the algorithm on an $n$-vertex graph is $2^{O(k^5\\log k)}\\cdot n^5$, and this is the first fixed-parameter algorithm for Graph Isomorphism parameterized by treewidth.\n  Our algorithm in fact solves the more general canonization problem. We namely design a procedure working in $2^{O(k^5\\log k)}\\cdot n^5$ time that, for a given graph $G$ on $n$ vertices, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0818","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"}