{"paper":{"title":"An Explicit Construction of Optimal Dominating Sets in Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"M. Alambardar Meybodi, M.R. Hooshmandasl, P. Sharifani","submitted_at":"2017-07-20T12:24:40Z","abstract_excerpt":"A dominating set in a graph $G$ is a subset of vertices $D$ such that every vertex in $V\\setminus D$ is a neighbor of some vertex of $D$. The domination number of $G$ is the minimum size of a dominating set of $G$ and it is denoted by $\\gamma(G)$. Also, a subset $D$ of a graph $G$ is a $[ 1 , 2 ] $-set if, each vertex $v \\in V \\setminus D$ is adjacent to either one or two vertices in $D$ and the minimum cardinality of $[ 1 , 2 ] $-dominating set of $G$, is denoted by $\\gamma_{[1,2]}(G)$. Chang's conjecture says that for every $16 \\leq m \\leq n$, $\\gamma(G_{m,n})= \\left \\lfloor\\frac{(n+2)(m+2)}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06471","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"}