Chromatic number is Ramsey distinguishing

A graph G is Ramsey for a graph H if every colouring of the edges of G in two colours contains a monochromatic copy of H. Two graphs H 1 and H 2 are Ramsey equivalent if any graph G is Ramsey for H 1 if and only if it is Ramsey for H 2. A graph parameter s is Ramsey distinguishing if s ( H 1 ) ≠ s ( H 2 ) implies that H 1 and H 2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing.