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The Minimum Sum Coloring Problem (MSCP) is derived from the Graph ColoringProblem (GCP) by associating a weight to each color. The aim of MSCP is to finda coloring solution of a graph such that the sum of color weights is minimum.MSCP has important applications in fields such as scheduling and VLSI design.We propose in this paper new upper bounds of the chromatic strength, i.e. theminimum number of colors in an optimal solution of MSCP, based on anabstraction of all possible colorings of a graph called motif. Experimentalresults on standard benchmarks show that our new bounds are significantlytighter than the previous bounds in general, allowing to reduce substantiallythe search space when solving MSCP .

Sum Coloring : New upper bounds for the chromatic strength