On a Combinatorial Problem of Erdös and Hajnal

Abstract

In this note we consider some problems related to the following question: What is the smallest integer m(n) for which there exists a family Fn of sets A1, A2,…, Am(n) with the following properties, (i) each member of Fn has n elements and (ii) if S is a set which meets each member of Fn, then S contains at least one member of Fn?Erdős and Hajnal [1] observed thatand that m(l) = 1, m(2) = 3, m(3) = 7.