## 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.)

Zbl 0865.05071
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