Let G=(V,E) be a graph with V={1,2,...,n}. We'll assume G has the following property:

For every $\displaystyle Y \subset V $ with $\displaystyle |Y| = n-2 $ , there exist distinct sets $\displaystyle F_1 , F_2 \in E $ inducing the same subet of Y : $\displaystyle F_1 \cap Y = F_2 \cap Y $ (i.e.- $\displaystyle F_1,F_2$ have a common vertex).

Show that $\displaystyle |E| \ge \lceil 3(n-1)/2 \rceil $ .

I really need help in this one.

Thanks in advance!