'Royal College of Obstetricians & Gynaecologists (RCOG)'
Abstract
The k-colour bipartite Ramsey number of a bipartite graph H is the least integer n for which
every k-edge-coloured complete bipartite graph Kn,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 Gy´arf´as and Lehel, who determined the 2-colour Ramsey number of paths. In
this paper we determine asymptotically the 3-colour bipartite Ramsey number of paths and (even)
cycles
