Adjoining edges to $G\mathbin{\square}H$ to construct a minimal dominating set of size $γ(G)γ(H)$

Abstract

edges to the Cartesian product G H such that a minimal dominating set D of size γ(G)γ(H) emerges. We hypothesize that D is also a minimum dominating set for the resulting graph and show that this implies Vizing's conjecture.