Solution:

We will prove that $G \geq R$. For each polygon $\mathcal{P}$ with all red vertices we can correspond a polygon with one green vertex (namely we can add the green vertex to the set of vertices of $\mathcal{P}$). Thus $G \geq R$. However, $G > R$ since the triangles with one green vertex can't be corresponded to some polygon whose all vertices are red.