Problem:
Let k>=3 be an integer , and let G be a plane graph of order n(>=k) and size m.
a) If the length of every cycle is at least k, then determine an upper bound B for m in terms of n and k.
b) Show that the bound B obtained in a) is sharp by determining for arbitrary k>=3, a plane graph G of order n and size B, every cycle of which has length at least k.