An extremal problem in graph theory

p r) the complete, r-chromatic graph with p, vertices of the i-th colour iii which everytwo vertices of different _colour are adjacent . Vertices of our graphs will be denoted by x, !! edges by (x, y) . The valence r(x) of x is the number of edges adjacent to x . Denote by m (-n ; p) the smallest integer so that every G (n ; vu . (n ; p)) contains a If,, . Turán [6] (comp. also [7]) determined ill ()) ; p) and also showed that the only G(n ; ill, (n ; p) -1) which contains no K.,, is If (Ill,, . . . , vn,,, , ), where