On the number of edges of quadrilateral-free graphs

Abstract

If a graph has q2 + q + 1 vertices (q > 13), e edges and no 4-cycles then e ≤ 1/2q(q + 1)2. Equality holds for graphs obtained from finite projective planes with polarities. This partly answers a question of Erdos from the 1930's. © 1996 Academic Press, Inc.