{"paper":{"title":"Computing the metric dimension by decomposing graphs into extended biconnected components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Duygu Vietz, Egon Wanke, Stefan Hoffmann","submitted_at":"2018-06-27T10:12:55Z","abstract_excerpt":"A vertex set $U \\subseteq V$ of an undirected graph $G=(V,E)$ is a $\\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \\in V$ there is a vertex $w \\in U$ such that the distances between $u$ and $w$ and the distance between $v$ and $w$ are different. The $\\textit{Metric Dimension}$ of $G$ is the size of a smallest resolving set for $G$. Deciding whether a given graph $G$ has Metric Dimension at most $k$ for some integer $k$ is well-known to be NP-complete. Many research has been done to understand the complexity of this problem on restricted graph classes. In this paper, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10389","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"}