{"paper":{"title":"Solving a Conjecture on Identification in Hamming Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tero Laihonen, Tuomo Lehtil\\\"a, Ville Junnila","submitted_at":"2018-05-04T10:02:06Z","abstract_excerpt":"Identifying codes in graphs have been widely studied since their introduction by Karpovsky, Chakrabarty and Levitin in 1998. In particular, there are a lot of results regarding the binary hypercubes, that is, the Hamming graphs $K_2^n$. In 2008, Gravier et al. started investigating identification in $K_q^2$. Goddard and Wash, in 2013, studied identifying codes in the general Hamming graphs $K_q^n$. They stated, for instance, that $\\gamma^{ID}(K_q^n)\\leq q^{n-1}$ for any $q$ and $n\\geq3$. Moreover, they conjectured that $\\gamma^{ID}(K_q^3)=q^2$. In this article, we show that $\\gamma^{ID}(K_q^3)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01693","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"}