{"paper":{"title":"(Total) Domination in Prisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jernej Azarija, Michael A. Henning, Sandi Klav\\v{z}ar","submitted_at":"2016-06-27T07:15:23Z","abstract_excerpt":"With the aid of hypergraph transversals it is proved that $\\gamma_t(Q_{n+1}) = 2\\gamma(Q_n)$, where $\\gamma_t(G)$ and $\\gamma(G)$ denote the total domination number and the domination number of $G$, respectively, and $Q_n$ is the $n$-dimensional hypercube. More generally, it is shown that if $G$ is a bipartite graph, then $\\gamma_t(G \\square K_2) = 2\\gamma(G)$. Further, we show that the bipartite condition is essential by constructing, for any $k \\ge 1$, a (non-bipartite) graph $G$ such that $\\gamma_t (G \\square K_2 ) = 2\\gamma(G) - k$. Along the way several domination-type identities for hype"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08143","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"}