BOUNDED VERTEX COLORINGS OF GRAPHS

A bounded vertex coloring of a graph G is a usual vertex coloring in which each color is used at most k times (where k is a given number). The bounded chromatic number gamma(k)(G) of G is the smallest number of colors such that G admits a bounded coloring. Upper and lower bounds on gamma(k)(G) are given in terms of k, the number n of vertices, the usual chromatic number gamma(G) and the maximum degree DELTA(G) of G. Complexity of bounded vertex coloring is discussed and severaL classes of graphs for which this problem is polynomially solvable are identified.