The tripartite Ramsey numbers r<inf>t</inf>(C<inf>4</inf>;2) and r<inf>t</inf>(C<inf>4</inf>;3)

Abstract

© 2015, Forum-Editrice Universitaria Udinese SRL. All rigths reserved. The k-colored tripartite Ramsey numbers rt(G; k) is the smallest positive integer n such that any k-coloring of lines of a complete tripartite graph Kn,n,nthere always exists a monochromatic subgraph isomorphic to G. When G is C4it is known, but unpublished in a journal, that rt(C4; 2) = 3. In this paper we simplify the proof of rt(C4; 2) = 3 and show the new result that rt(C4; 3) = 7.