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Vizing-like conjecture for the upper domination of Cartesian products of graphs – the proof. (English) Zbl 1074.05065

Summary: We prove the following conjecture of R. J. Nowakowski and D. F. Rall [Discuss. Math., Graph Theory 16, 53–79 (1996; Zbl 0865.05071)]: For arbitrary graphs \(G\) and \(H\) the upper domination number of the Cartesian product \(G\square H\) is at least the product of their upper domination numbers, in symbols: \(\Gamma(G\square H)\geq \Gamma(G)\Gamma(H)\).

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

Citations:

Zbl 0865.05071
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