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{\bf Bo\v{s}tjan Bre\v{s}ar}
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{\bf Vizing-like Conjecture for the Upper Domination of Cartesian Products of Graphs -- The Proof}
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In this note we prove the following conjecture of Nowakowski and Rall:
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: $\Gamma(G \,\square \, H)\ge
\Gamma(G)\Gamma(H).$

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