A note on the monotonicity of mixed Ramsey numbers

For two graphs, G and H , an edge coloring of a complete graph is ( G , H ) -good if there is no monochromatic subgraph isomorphic to G and no rainbow subgraph isomorphic to H in this coloring. The set of numbers of colors used by ( G , H ) -good colorings of K n is called a mixed Ramsey spectrum. This note addresses a fundamental question of whether the spectrum is an interval. It is shown that the answer is “yes” if G is not a star and H does not contain a pendant edge.