A Note on Uniquely lntersectable Graphs

摘要

The following conjecture of Alter and Wang is proven. Consider the intersection graphGn,m,n⩾2m, determined by the family of allm‐element subsets of ann‐element set. Then any realization ofGn,mas an intersection graph by a family of sets satisfies ∪iAi⩾n; and if ∪iAi=n, thenFmust be the family of allm‐element su