{"paper":{"title":"Twin domination number of Tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dorota Osula, Rita Zuazua","submitted_at":"2017-02-02T12:38:03Z","abstract_excerpt":"Let $D=(V,A)$ be a digraph. A subset $S$ of $V$ is called a twin dominating set of $D$ if for every vertex $v\\in V-S$, there exists vertices $u_1,u_2 \\in S$ such that $(v,u_1)$ and $(u_2,v)$ are arcs in $D$. The minimum cardinality of a twin dominating set in $D$ is called the twin domination number of $D$ and is denoted by $\\gamma ^{*}(D)$.\n  The upper orientable twin domination number of a graph $G$ is $DOM^{*}(G)=\\max\\{ \\gamma ^{*}(D)|D \\ \\text{is an orientation of G} \\}.$ It has been conjectured that for the complete graph $K_n$ with $n\\geq 8$, $DOM^{*}(K_n)=\\left\\lceil \\frac{n+1}{2}\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00646","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"}