The cost chromatic number and hypergraph parameters
Gábor Bacsó, Źsolt Tuza · Discussiones Mathematicae Graph Theory · 2006
In a graph, by deflnition, 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.