On the maximum number of edges in a c4-free subgraph of qn

For the maximum number f(n) of edges in a C4-free subgraph of the n-dimensional cube-graph Qn we prove f(n) ≥ 1/2(n +√n)2n−1 for n = 4r, and f(n) ≥ 1/2(n +0.9√n)2n−1 for all n ≥ 9. This disproves one version of a conjecture of P. Erdos. © 1995 John Wiley & Sons, Inc.