a1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2975, USA and Mathematical Institute of the Hungarian Academy of Sciences, PO Box 127, Budapest 1364, Hungary
Let ex(n, K3,3) denote the maximum number of edges of a K3,3-free graph on n vertices. Improving earlier results of Kővári, T. Sós and Turán on Zarankiewicz' problem, we obtain that Brown's example for a maximal K3,3-free graph is asymptotically optimal. Hence .
(Received January 05 1995)
(Revised March 09 1995)