{"paper":{"title":"2-connected equimatchable graphs on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eduard Eiben, Michal Kotrb\\v{c}\\'ik","submitted_at":"2013-12-12T09:19:33Z","abstract_excerpt":"A graph $G$ is equimatchable if any matching in $G$ is a subset of a maximum-size matching. It is known that any $2$-connected equimatchable graph is either bipartite or factor-critical. We prove that for any vertex $v$ of a $2$-connected factor-critical equimatchable graph $G$ and a minimal matching $M$ that isolates $v$ the graph $G\\setminus(M\\cup\\{ v\\})$ is either $K_{2n}$ or $K_{n,n}$ for some $n$. We use this result to improve the upper bounds on the maximum size of $2$-connected equimatchable factor-critical graphs embeddable in the orientable surface of genus $g$ to $4\\sqrt g+17$ if $g\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3423","kind":"arxiv","version":1},"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"}