{"paper":{"title":"Upper Domination: towards a dichotomy through boundary properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bernard Ries, Hassan AbouEisha, J\\'er\\^ome Monnot, Shahid Hussain, Vadim Lozin, Viktor Zamaraev","submitted_at":"2016-09-06T12:01:56Z","abstract_excerpt":"An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes of graphs defined by finitely many forbidden induced subgraphs and conjecture that the problem admits a dichotomy in this family, i.e. it is either NP-hard or polynomial-time solvable for each class in the family. A helpful tool to study the complexity of an algorithmic problem on finitely defined classes of graphs is the notion of boundary classes. However, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01510","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"}