Tripartite Ramsey numbers for paths

Abstract

Abstract In this article, we study the tripartite Ramsey numbers of paths. We show that in any two‐coloring of the edges of the complete tripartite graph K ( n , n , n ) there is a monochromatic path of length (1 − o (1))2 n . Since R ( P 2 n +1 , P 2 n +1 )=3 n , this means that the length of the longest monochromatic path is about the same when two‐colorings of K 3 n and K ( n , n , n ) are considered. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 164–174, 2007