The genus of the Cartesian product of two graphs

Upper and lower bounds are given for the genus, γ(G₁ × G₂), of the Cartesian product of arbitrary graphs G₁ and G₂, in terms of the genera γ(G₁) and γ(G₂). These bounds are then used to obtain asymptotic results for the cases in which G₁ and G₂ are both regular complete k-partite graphs.