{"paper":{"title":"On the $k$-partition dimension of graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro Estrada-Moreno","submitted_at":"2018-05-13T22:33:23Z","abstract_excerpt":"As a generalization of the concept of the partition dimension of a graph, this article introduces the notion of the $k$-partition dimension. Given a nontrivial connected graph $G=(V,E)$, a partition $\\Pi$ of $V$ is said to be a $k$-partition generator for $G$ if any pair of different vertices $u,v\\in V$ is distinguished by at least $k$ vertex sets of $\\Pi$, \\emph{i.e}., there exist at least $k$ vertex sets $S_1,\\ldots,S_k\\in\\Pi$ such that $d(u,S_i)\\ne d(v,S_i)$ for every $i\\in\\{1,\\ldots,k\\}$. A $k$-partition generator for $G$ with minimum cardinality among all their $k$-partition generators is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04966","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"}