We prove an upper bound for the number of edges a C4-free graph on q2+q vertices can contain for q even. This upper bound is achieved whenever there is an orthogonal polarity graph of a plane of even order q. © 2013 Elsevier Inc.
Firke, F. A., Kosek, P. M., Nash, E. D., & Williford, J. (2013). Extremal graphs without 4-cycles. Journal of Combinatorial Theory. Series B, 103(3), 327–336. https://doi.org/10.1016/j.jctb.2013.01.001