{"paper":{"title":"New Bounds on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ari Cukierman, Gexin Yu","submitted_at":"2011-10-05T20:28:53Z","abstract_excerpt":"For a graph, $G$, and a vertex $v \\in V(G)$, let $N[v]$ be the set of vertices adjacent to and including $v$. A set $D \\subseteq V(G)$ is a vertex identifying code if for any two distinct vertices $v_1, v_2 \\in V(G)$, the vertex sets $N[v_1] \\cap D$ and $N[v_2] \\cap D$ are distinct and non-empty. We consider the minimum density of a vertex identifying code for the infinite hexagonal grid. In 2000, Cohen et al. constructed two codes with a density of $3/7 \\approx 0.428571$, and this remains the best known upper bound. Until now, the best known lower bound was $12/29 \\approx 0.413793$ and was pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1097","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"}