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Multipartite Graph Theoretic Ramsey Numbers. Part I: Set Numbers

in Discrete Mathematics, Volume 283 (2004), pages 37-43
by AP Burger1 & JH van Vuuren2

Abstract

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 vertices per partite set in the larger graph and then seeking the minimum number of such partite sets that would ensure the occurrence of certain specified monochromatic multipartite subgraphs.

An electronic version of the complete paper may be obtained here: [pdf].

Affiliations

1 Department of Mathematics, Applied Mathematics & Astronomy, University of South Africa, PO Box 392, Pretoria, 0003, Republic of South Africa, email: alewynburger@hotmail.com
2 Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa, fax: +27 21 8083778, email: vuuren@sun.ac.za

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