An r-graph is a graph whose basic elements are its vertices and r-tuples . It is proved that to every 1 and r there is an e(l, r) so that for n > no every r-graph of n vertices and n'-E(i, r) r-tuples contains r . /vertices P),I5 j < r, l < i < l, so that all the r-tuples (x i ,( 1 ), xi2 (2 ) ' . . . , x1 (')) occur in the r-graph . By an r-graph G (')(r >_ 2) we shall mean a graph whose basic...