Chromatic Ramsey numbers

Suppose G is a graph. The chromatic Ramsey number r(c)(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: for any 2-colouring of the edges of F there is a monochromatic subgraph isomorphic to G. Let M-n = min{r(c)(a) : chi(G) = n} It was conjectured by Burr et al. (1976) that M-n = (n - 1)(2) + 1. This conjecture has been confirmed previously for n less than or equal to 4. In this paper, we shall prove that the conjecture is true for n = 5. We shall also improve the upper bounds for M-6 and M-7. (C) 1998 Elsevier Science B.V. All rights reserved.