On the cost-chromatic number of graphs Original Research Article

We consider vertex colorings in which each color has an associated cost, incurred each time the color is assigned to a vertex. For a given set of costs, a minimum-cost coloring is a vertex coloring which makes the total cost of coloring the graph as small as possible. The cost-chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum-cost coloring of the graph. We establish upper bounds on the cost-chromatic number, show that trees and planar blocks can have arbitrarily large cost-chromatic number, and show that cost-chromatic number is not monotonic with subgraph inclusion