Chromatic number is Ramsey distinguishing
Michael Savery · Journal of Graph Theory · 2021
Abstract A graph is Ramsey for a graph if every colouring of the edges of in two colours contains a monochromatic copy of . Two graphs and are Ramsey equivalent if any graph is Ramsey for if and only if it is Ramsey for . A graph parameter is Ramsey distinguishing if implies that and 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.