Some extremal problems on gamma-graphs

Let f(r)(n;k,s) denote the smallest t for which every r-graph with n vertices and t r-tuples contains a subgraph with k vertices and at least s r-tuples. It is proved that for integers k>r and s>1 there exists a positive constant ck,s such that f(r)(n;k,s)>ck,sn(rs−k)/(s−1). This inequality follows from a counting argument. Unfortunately a number of misprints make the proof seem incorrect. Inequality (1) ensures that there exists an r-graph H0(r) in M such that b(H0(r))