{"paper":{"title":"On the Existence of $t$-Identifying Codes in Undirected De Bruijn Graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Victoria Horan","submitted_at":"2015-08-03T12:56:39Z","abstract_excerpt":"This paper proves the existence of $t$-identifying codes on the class of undirected de Bruijn graphs with string length $n$ and alphabet size $d$, referred to as $\\mathcal{B}(d,n)$. It is shown that $\\mathcal{B}(d,n)$ is $t$-identifiable whenever $d \\geq 3$ and $n \\geq 2t$, and $t \\geq 1$. We also show that $\\mathcal{B}(d,n)$ is $t$-identifiable if either $d \\geq 3$, $n \\geq 3$, and $t=2$, or if $d = 2$, $n \\geq 3$, and $t=1$. The remaining cases remain open. Additionally, we show that the eccentricity of the undirected non-binary de Bruijn graph is $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00403","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"}