Let G=(V,E) be a graph with V={1,2,...,n}. We'll assume G has the following property:
For every  Y \subset V with  |Y| = n-2 , there exist distinct sets  F_1 , F_2 \in E inducing the same subet of Y :  F_1 \cap Y = F_2 \cap Y (i.e.-  F_1,F_2 have a common vertex).
Show that  |E| \ge \lceil 3(n-1)/2 \rceil .

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