A note on the grid Ramsey problem

Publication date: 27 September 2017

Abstract: The grid Ramsey number

G (r)

is the smallest number

n

such that every edge-colouring of the grid graph

G a m m a_{n, n} : = K_{n} i m e s K_{n}

with

r

colours induces a rectangle whose parallel edges receive the same colour. We show

, slightly improving the currently best known upper bound due to Gy'arf'as.

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