The Erdös-Ko-Rado Theorem for Small Families

Abstract Let t be a fixed positive integer and c a real constant, 0 1 2 . We prove that for n sufficiently large each family A of cn-element subsets of [n] having | A | = n contains a t-intersecting subfamily A ′ ⊆ A with | A ′|>/ cn(1 − o(1)).