P. Frankl: Let F be a family of k-subsets of an n-set, containing no s+1 pairwise disjoint edges. Then for n > (2s+1)k-s one has

| F| \leq {n \choose k} - {n-s \choose k}.

The bound is best possible and confirms a conjecture of Erdős dating back to 1965. The main tool of the compact proof is an extension of the intersecting shadow theorem of Katona.