Suppose and . Suppose is a collection of all -element subsets of and let be the collection of all -element subsets of . Build a bipartite graph with by joining to if and only if
Suppose is a collection of subsets of such that for all distinct and . Show that .
Hint 1: First show has a matching hitting every element of
Hint 2: If consists of all subsets of of size then this upper bound is reached.