Domination number of Cartesian product through space projections

In 1968, Vizing conjectured that for every pair of graphs X and Y, the inequality gamma(X square Y) > gamma(X)gamma(Y) holds, where gamma stands for the domination number and X square Y is the Cartesian product of X and Y. In a breakthrough result, Clark and Suen [Electron. J. Combin. 7 (2000) #N4] proved that gamma(X square Y) > 1/2 gamma(X)gamma(Y). In this paper, a lower bound for gamma(X square Y square Z) is obtained using projections in the space. It is shown how the obtained bound implies the mentioned result of Clark and Suen.