Zero-sum delta-systems and multiple copies of graphs

A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence d(1) greater than or equal to d(2) greater than or equal to ... greater than or equal to d(n) and t 2 be a prime. Let m = gcd{t, d(i) - d(j); 1 less than or equal to i < j less than or equal to n} and set [GRAPHICS] Then R(tG,Z(t)) = t(n + d) - d, where R is the zero-sum Ramsey number. This settles, almost completely, problems raised in [Bialostocki & Dierker, J Graph Theory, 1994; Y. Care, J Graph Theory, 1991]. (C) 1999 John Wiley & Sons,Inc. J Graph Theory 32:207-216,1999.