Cross-intersecting families of finite sets

It is proved that A is a family of a-element sets and B is a family of b-element sets on the common undelying set [n], and A ∩ B ≠ ∅ for all A ∈ A, B ∈ B (i.e., cross-intersecting), and n ⩾ a + b, , and then there exists an element xϵ[n] such that it belongs to all members of A and B. This is an extension of a result of Hilton and Milner who generalized the Erdös-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.