Research collection / 01

Non-isomorphic graphs have distinct vertex-Ramsey classes

For a graph H, its k-colour vertex Ramsey class is the set of all graphs G such that any colouring of the vertices of G in k colours results in a monochromatic (induced) copy of H. The authors prove that for any k, Ramsey classes of any non-isomorphic graphs are distinct.

Present ordinary and induced vertex-Ramsey class separation through colouring constructions, repetition, block reduction and recursive separators, displaying every original claim, coverage replacement and immediate supplier together with the complete local helper chains.