{"paper":{"title":"On the Metric Dimension of $K_a \\times K_b \\times K_c$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Gerold J\\\"ager, Valentin Gledel","submitted_at":"2024-08-30T12:16:22Z","abstract_excerpt":"In this work we determine the metric dimension of $ K_a \\times K_b \\times K_c$ for all $a,b,c\\in \\mathbb N$ with $ a \\le b \\le c $ as follows. For $3a<b+c$ and $2b \\le c$, this value is $c-1$, for $3a<b+c$ and $2b > c$, it is $\\left \\lfloor \\frac{2}{3}(b+c-1) \\right \\rfloor$, and for $3a=b+c$, it is $\\left \\lfloor \\frac{a+b+c}{2} \\right \\rfloor -1 $. The only open case is $3a>b+c$, where two values are possible, namely $\\left \\lfloor \\frac{a+b+c}{2} \\right \\rfloor -1 $ and $\\left \\lfloor \\frac{a+b+c}{2} \\right \\rfloor $. This result extends previous results of C\\'acere et al., who computed the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.17229","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.17229/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}