2019•UCL Discovery (University College London)Requires access

3‐Color bipartite Ramsey number of cycles and paths

Matija Bucić, Shoham Letzter, Benny Sudakov

Abstract

The k-colour bipartite Ramsey number of a bipartite graph H is the least integer n for which \nevery k-edge-coloured complete bipartite graph Kn,n contains a monochromatic copy of H. The \nstudy of bipartite Ramsey numbers was initiated, over 40 years ago, by Faudree and Schelp and, \nindependently, by Gy´arf´as and Lehel, who determined the 2-colour Ramsey number of paths. In \nthis paper we determine asymptotically the 3-colour bipartite Ramsey number of paths and (even) \ncycles.

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Key concepts: Bipartite graph, Ramsey's theorem, Combinatorics, Mathematics, Complete bipartite graph, Monochromatic color, Edge-transitive graph, Integer (computer science)