3‐Color bipartite Ramsey number of cycles and paths. Issue 4 (7th May 2019) - Bucić, Matija; Letzter, Shoham; Sudakov, Benny
Abstract: The k ‐color bipartite Ramsey number of a bipartite graph H is the least integer n for which every k ‐edge‐colored complete bipartite graph K n, n contains a monochromatic copy of H . The study of bipartite Ramsey numbers was initiated, over 40 years ago, by Faudree and Schelp and, independently, by Gyárfás and Lehel, who determined the 2‐color Ramsey number of paths. In this paper we determine asymptotically the 3‐color bipartite Ramsey number of paths and (even) cycles.