Let G be a simple, connected, planar graph with n\geq3 vertices, m edges and r faces. Assume that every vertex of G has degree at least 3.

a) Show that 2m\geq3n and use Euler's formula to deduce that 2\leq r-\frac{m}{3}.
b) Assume now that all faces of G have degree either 5 or 6. Let p and h the number of faces of degree 5 and 6, respectively, so r=p+h. Show that 2m=5p+6h. Use this and the previous part of the question to show p\geq12 in this case.

To bring you up to speed with what I know, I have no idea how to show 2m\geq3n in part a), but I do know that n-m+r=2, so I'm on the cusp of deducing the other thing in part a), but I just can't quite get it.

For part b) I know that \sum^{r}_{i=1}deg(F_i)=2m (where the F_i's are the faces in G, so again I'm kind of halfway there, I just can't quite get what the question's wanting cheers for any help in advance.