A Note on Uniquely lntersectable Graphs

The following conjecture of Alter and Wang is proven. Consider the intersection graph G_n,m,n?2m, determined by the family of all m-element subsets of an n-element set. Then any realization of G_n,m as an intersection graph by a family of sets satisfies |∪_iA_i|?n; and if |∪_iA_i|=n, then F must be the family of all m-element subsets of ∪_iA_i.