Ramsey Set Numbers in Balanced Complete Multipartite Graphs

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Journal of Combinatorial Mathematics and Combinatorial Computing


One natural extension of classical Ramsey numbers to multipartite graphs is to consider 2-colorings of the complete multipartite graph consisting of n parts, each of size k, denoted K n×k . We may then ask for the minimum integer n such that K n×k →{G,H} for two given graphs G and H. We study this number for the the cases when C and H are paths or cycles and show some general bounds and relations to classical Ramsey theory.