Weakened Ramsey numbers

Classical Ramsey numbers r = r,(G) ask for the smallest number r such that every t-coloring of the edges of the complete graph K-r contains a monochro matic copy of a given graph G. Weakened Ramsey numbers R-s,R-t(G) ask in ev ery t-coloring of K-R for a copy of G with at most s colors, s < t. First r esults are given for s = t - 1. (C) 1999 Elsevier Science B.V. All rights r eserved.