M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 1999. Chap. 20 gives a simple proof of the upper bound (n/4)(sqrt(4n-3)+1) and of the fact that it is asymptotically tight. - Christopher E. Thompson, Aug 14 2001
P. Kovari, V. T. Sos, and P. Turan. On a problem of K. Zarankiewicz, Colloq. Math. (4th ed.), 3 (1954), pp. 50-57.
Brendan McKay, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. R. J. Clapham, A. Flockhart, and J. Sheehan, Graphs without four-cycles, J. Graph Theory 13 (1) (1989) 29-47
Zoltán Füredi, Quadrilateral-free graphs with maximum number of edges, Extended abstract, Proceedings of the Japan Workshop on Graph Th. and Combinatorics, University, Yokohama, Japan 1994, pp. 13-22 (see Section 6).
a(n) <= n^(3/2)*(1/2 + o(1)) [Kovari, Sos, Turan]. But the upper bound mentioned in the Aigner-Ziegler reference (see above) is stronger. - N. J. A. Sloane, Mar 07 2022
