{"paper":{"title":"Shortest Non-trivial Cycles in Directed and Undirected Surface Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CG","authors_text":"Kyle Fox","submitted_at":"2011-11-29T21:24:21Z","abstract_excerpt":"Let G be a graph embedded on a surface of genus g with b boundary cycles. We describe algorithms to compute multiple types of non-trivial cycles in G, using different techniques depending on whether or not G is an undirected graph. If G is undirected, then we give an algorithm to compute a shortest non-separating cycle in 2^O(g) n log log n time. Similar algorithms are given to compute a shortest non-contractible or non-null-homologous cycle in 2^O(g+b) n log log n time. Our algorithms for undirected G combine an algorithm of Kutz with known techniques for efficiently enumerating homotopy clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6990","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"}