{"paper":{"title":"Clustering to Given Connectivities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dimitrios M. Thilikos, Petr A. Golovach","submitted_at":"2018-03-26T09:38:02Z","abstract_excerpt":"We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a sequence $\\Lambda=\\langle \\lambda_{1},\\ldots,\\lambda_{t}\\rangle$ of positive integers and we ask whether it is possible to remove at most $k$ edges from $G$ such that the resulting connected components are {\\sl exactly} $t$ and their corresponding edge connectivities are lower-bounded by the numbers in $\\Lambda$. We prove that this problem, parameterized by $k$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09483","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"}