{"paper":{"title":"Resolving sets and semi-resolving sets in finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcella Tak\\'ats, Tam\\'as H\\'eger","submitted_at":"2012-07-23T18:11:10Z","abstract_excerpt":"We show that the metric dimension of a finite projective plane of order $q\\geq 23$ is $4q-4$, and describe all resolving sets of that size. Let $\\tau_2$ denote the size of the smallest double blocking set in $\\mathrm{PG}(2,q)$, the Desarguesian projective plane of order $q$. We prove that for a semi-resolving set $S$ in the incidence graph of $\\mathrm{PG}(2,q)$, $|S|\\geq \\min \\{2q+q/4-3, \\tau_2-2\\}$ holds. In particular, if $q\\geq9$ is a square, then the smallest semi-resolving set in $\\mathrm{PG}(2,q)$ has size $2q+2\\sqrt{q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5469","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"}