{"paper":{"title":"Classification of Minimal Separating Sets in Low Genus Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CO","authors_text":"Austin K. Williams, J. J. P. Veerman, Victor Rielly, William J. Maxwell","submitted_at":"2017-01-17T00:40:23Z","abstract_excerpt":"Consider a surface $S$ and let $M\\subset S$. If $S\\setminus M$ is not connected, then we say $M$ \\emph{separates} $S$, and we refer to $M$ as a \\emph{separating set} of $S$. If $M$ separates $S$, and no proper subset of $M$ separates $S$, then we say $M$ is a \\emph{minimal separating set} of $S$. In this paper we use methods of computational combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus $g=2$ and $g=3$. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04496","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"}