On two set-systems with restricted cross-intersections

Abstract If A 1 , …, A m ; B 1 , …, B m are finite sets such that for l ⩾ t ⩾ 0 and any r , s , we have | A i | ⩽ r , | B i | ⩽ s and | i ∩ B i | ⩽ t for 1 ⩽ i ⩽ m and | A i ∩ B i | > l for 1 ⩽ i j ⩽ m , what is the maximum value that m can attain? In this paper we answer this question of Furedi and extend an inequality of Bollobas.im]0658.TIF