Vizing-like conjecture for the upper domination of Cartesian products of graphs - The proof

Abstract

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 □ H is at least the product of their upper domination numbers, in symbols: Γ(G □ H) ≥ Γ(G)Γ(H).