Let uk(G, p) be the maximum over all k-vertex graphs F of by how much the number of induced copies of F in G differs from its expectation in the Erdős-Rényi random graph with edge probability p. This may be viewed as a measure of how close G is to being p-quasirandom. Our main result is that, for fixed k ≥ 4 and 0 < p < 1, the minimum of uk(G, p) over n-vertex graphs has order of magnitude Θ(n ...
