We investigate the effect of adding $ω_2$ Cohen reals on graphs on $ω_2$, in particular we show that $ω_2 \to (ω_2, ω: ω)^2$ holds after forcing with $\mathsf{Add}(ω, ω_2)$ in a model of $\mathsf{CH}$. We also prove that this results is in a certain sense optimal as $\mathsf{Add}(ω, ω_2)$ forces that $ω_2 \not\to (ω_2, ω: ω_1)^2$.
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