The chromatic difference sequence of a graph

Abstract Let α k ( G ) denote the maximum number of vertices in a k -colorable subgraph of G . Set α k (G)= α k ( G )− α ( k −1) ( G ). The sequence a 1 ( G ), a 2 ( G ),… is called the chromatic difference sequence of the graph G . We present necessary and sufficient conditions for a sequence to be the chromatic difference sequence of some 4-colorable graph.