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On the cost chromatic number of outerplanar, planar, and line graphs

John MitchemPatrick MorrissEdward Schmeichel — 1997

Discussiones Mathematicae Graph Theory

We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. 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 show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and construct...

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