Given two graphs $G=(V_1,E_1)$ and $H=(V_2,E_2)$, the tensor product of $G$ and $H$ is the graph $G \times H = (V,E)$, where $V=V_1 \times V_2$ is the Cartesian product of the $V_i$ and $ (u,v) \ E \ (u',v') \Leftrightarrow u E_1 u' \wedge v E_2 v'$.

Is anyone aware of a characterization of which $G,H$ give rise to a planar tensor product $G \times H$?