Multipartite Ramsey Numbers.
David P. Day, Wayne Goddard, Michael A. Henning, Henda C. Swart · 2001
For a graph G, a partiteness k ≥ 2 and a number of colours c, we define the multipartite Ramsey number rc k (G) as the minimum value m such that, given any colouring using c colours of the edges of the complete balanced k-partite graph with m vertices in each partite set, there must exist a monochromatic copy of G. We show that the question of the existence of rc k (G) is tied up with what monochromatic subgraphs are forced in a ccolouring of the complete graph Kk. We then calculate the values for some