  We investigate the effect of adding $\omega_2$ Cohen reals on graphs on
$\omega_2$, in particular we show that $\omega_2 \to (\omega_2, \omega :
\omega)^2$ holds after forcing with $\mathsf{Add}(\omega, \omega_2)$ in a model
of $\mathsf{CH}$. We also prove that this results is in a certain sense optimal
as $\mathsf{Add}(\omega, \omega_2)$ forces that $\omega_2 \not\to (\omega_2,
\omega : \omega_1)^2$.
