Critical probabilities for site and bond percolation models

Any infinite graph G = (V, E) has a site percolation critical probability p (c)(site) and a bond percolation critical probability p(c)(bond). The well- known weak inequality p(c)(site) greater than or equal to p(c)(bond) is str engthened to strict inequality for a broad category of graphs G, including all the usual finite-dimensional lattices in two and more dimensions. The c omplementary inequality p(c)(site) less than or equal to 1 - (1 - p(c)(bond ))(Delta - 1) is proved also, where Delta denotes the supremum of the verte x degrees of G.