Remarks on a Paper by Y.Caro and R.Yuster on Turan Problem

Caro and Yuster (Electronic J.Comb 7 (2000)) studied a generalization of the Turan problem, where a certain function (instead of the size) of an F-free graph of order n has to be maximized. We prove that for a wide class of functions the asymptotics of the maximum is given by complete partite graphs.