On induced Folkman numbers

In 1970, Folkman proved that for any graph G there exists a graph H with the same clique number as G. In addition, any r -coloring of the vertices of H yields a monochromatic copy of G. For a given graph G and a number of colors r let f(G, r) be the order of the smallest graph H with the above properties. In this paper, we give a relatively small upper bound on f(G, r) as a function of the order of G and its clique number. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 40, 493–500, 2012 © 2012 Wiley Periodicals, Inc.