then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •, Yn-k+l and edges (x1 , xj), 1I ; (x1 , y), 1 i :!-< k 1, 1-yj :!5 n k + 1 clearly does not contain k independent edges . By an r-graph o(r) we shall mean a graph whose basic elements are its vertices and r-tuples ; for r = 2 we obtain the ordinary graphs . G (r) (n ; m) will denote an r-graph of n… CONTINUE READING