Lemma 3. Let r≥2 be an integer and let w maximize F_G on a nonempty finite K_r -free graph G . For every x≥1 and all vertex sets S,D with w(S),w(D)≤e^x , e_w(S,D)≤C_r g_x(w(S)), C_r=16r^2. The sets S and D need not be disjoint.