Abstract:We introduce a variant of the graph coloring problem, which we denote as Budgeted Coloring Problem (BCP). Given a graph G, an integer c and an ordered list of integers {b 1 , b 2 , . . . , b c }, BCP asks whether there exists a proper coloring of G where the i-th color is used to color at most b i many vertices. This problem generalizes two well-studied graph coloring problems, Bounded Coloring Problem (BoCP) and Equitable Coloring Problem (ECP) and as in the case of other coloring problems, it is NP-hard even… Show more
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