Geodesic
The cost chromatic number and hypergraph parameters
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 369-376

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In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
Keywords: graph coloring, cost chromatic number, intersection number of a hypergraph 
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Bacsó, Gábor; Tuza, Zsolt. The cost chromatic number and hypergraph parameters. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 369-376. http://geodesic.mathdoc.fr/item/DMGT_2006_26_3_a1/