{"paper":{"title":"The Fault-Tolerant Metric Dimension of Cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Duygu Vietz, Egon Wanke","submitted_at":"2019-04-07T16:26:33Z","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 distance between $u$ and $w$ and the distance between $v$ and $w$ are different. A resolving set $U$ is {\\em fault-tolerant} if for every vertex $u\\in U$ set $U\\setminus \\{u\\}$ is still a resolving set. {The \\em (fault-tolerant) Metric Dimension} of $G$ is the size of a smallest (fault-tolerant) resolving set for $G$. The {\\em weighted (fault-tolerant) Metric Dimension} for a given cost function $c: V \\longrig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04243","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"}