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Diagonal Ramsey Numbers in Multipartite Graphs |
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AP Burger1, PJP Grobler2, EH Stipp3 & JH van Vuuren3
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 sub-graphs are complete, balanced, multipartite graphs, instead of complete graphs as in the classical definition. Some small multipartite Ramsey numbers are found, while upper and lower bounds are established for others. Analytic arguments as well as computer searches are employed.
An electronic version of the complete paper may be obtained here: [ps] [pdf].
Affiliations
1 Department of Mathematics & Applied Mathematics, University of South Africa, PO Box 392, Pretoria,
0003, Republic of South Africa, email: alewynburger@mweb.co.za
2 School of Mathematical & Statistical Sciences, University of Natal, Durban, 4041, Republic of South Africa.
3 Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa,
fax: +27 21 8083778, email: vuuren@sun.ac.za