Ramsey numbers in complete balanced multipartite graphs. Part II: Size numbers

The notion of a graph theoretic Ramsey number is generalised by assuming that both the original graph whose edges are arbitrarily bi-coloured and the sought after monochromatic subgraphs are complete, balanced, multipartite graphs, instead of complete graphs as in the classical definition. We previously confined our attention to diagonal multipartite Ramsey numbers. In this paper, the definition of a multipartite Ramsey number is broadened still further, by incorporating off-diagonal numbers, fixing the number of partite sets in the larger graph and then seeking the minimum cardinality of such partite sets that would ensure the occurrence of certain specified monochromatic multipartite subgraphs. (C) 2004 Elsevier B.V. All rights reserved.