A variation of the graph coloring problem Given a set of colors $M$ and a graph $G=(V,E)$. Allocate the colors to minimize the number edges with same color on the two vertices of the edge (i.e. minimize pairs of adjoining vertices with same color.).

This problem is different from standard coloring problem. Could someone please provide some literature where this problem is studied?
If $|M| = 2$, this is the max-cut problem.