{"paper":{"title":"On Complexity of Isoperimetric Problems on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Amir Daneshgar, Ramin Javadi","submitted_at":"2010-09-03T16:00:57Z","abstract_excerpt":"This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\\it minimum normalized cuts}/{\\it isoperimteric numbers} defined through taking minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a {\\it partition}/{\\it subpartition}. Following the main result of [A. Daneshgar, {\\it et. al.}, {\\it On the isoperimetric spectrum of graphs and its approximations}, JCTB, (2010)], it is known"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0706","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"}