Possible Duplicate:
Proving component size based on number of edges and vertices.
Prove that if $G$ has more than $\dfrac{5n^2}{18}$ edges then $G$ has no connected component of size (number of vertices) between $\dfrac{n}{3}$ and $\dfrac{2n}{3}$.
I'm not even sure where to start nor what is being asked in regards to the connectedness of the graph. Is this question alluding to graphs with two or more components?