INEQUALITIES IN PROBABILITY-THEORY AND TURAN-TYPE PROBLEMS FOR GRAPHS WITH COLORED VERTICES

The "best" inequalities of type P{(zeta, eta) membership sign E} greater-than-or-equal-to f(P{zeta-membership sign D1},....,P{zeta-membership sign D(m)}) for independent and identically distributed random elements-zeta and eta can be reduced to Turan-type problems for graphs with colored vertices. In the present work we describe a finite algorithm for obtaining the asymptotical solution for an arbitrary problem of such type. In the case of two colors we obtain the final form of asymptotic solution without using the algorithm.