{"paper":{"title":"On the partition dimension of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ismael G. Yero, Juan A. Rodriguez-Velazquez, Magdalena Lemanska","submitted_at":"2011-10-24T17:38:27Z","abstract_excerpt":"Given an ordered partition $\\Pi =\\{P_1,P_2, ...,P_t\\}$ of the vertex set $V$ of a connected graph $G=(V,E)$, the \\emph{partition representation} of a vertex $v\\in V$ with respect to the partition $\\Pi$ is the vector $r(v|\\Pi)=(d(v,P_1),d(v,P_2),...,d(v,P_t))$, where $d(v,P_i)$ represents the distance between the vertex $v$ and the set $P_i$. A partition $\\Pi$ of $V$ is a \\emph{resolving partition} of $G$ if different vertices of $G$ have different partition representations, i.e., for every pair of vertices $u,v\\in V$, $r(u|\\Pi)\\ne r(v|\\Pi)$. The \\emph{partition dimension} of $G$ is the minimum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5289","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"}