  In perturbative expansion of field theories on a non-commutative geometry, it
is known that planar diagrams dominate when the non-commutativity parameter
$\theta$ goes to infinity. We discuss whether the ``planar dominance'' occurs
also in the case where $\theta$ is finite, but the external momentum goes to
infinity instead. While this holds trivially at the one-loop level, it is not
obvious at the two-loop level in particular in the presence of UV divergences.
We perform explicit two-loop calculations in the six-dimensional $\phi^3$
theory, and confirm that nonplanar diagrams after renormalization do vanish in
the above limit.
