{"paper":{"title":"Minimal resolving sets for the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Ashwin Ganesan","submitted_at":"2011-06-18T10:14:14Z","abstract_excerpt":"For a given undirected graph $G$, an \\emph{ordered} subset $S = {s_1,s_2,...,s_k} \\subseteq V$ of vertices is a resolving set for the graph if the vertices of the graph are distinguishable by their vector of distances to the vertices in $S$. While a superset of any resolving set is always a resolving set, a proper subset of a resolving set is not necessarily a resolving set, and we are interested in determining resolving sets that are minimal or that are minimum (of minimal cardinality). Let $Q^n$ denote the $n$-dimensional hypercube with vertex set ${0,1}^n$. In Erd\\\"os and Renyi (Erdos & Ren"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3632","kind":"arxiv","version":3},"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"}