Lower Bound for (Sum) Coloring Problem

19 Sep 2019 · Gondran Alexandre ENAC, Duchamp Vincent ENAC, Moalic Laurent Université de Haute-Alsace ·

The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition problem with additional constraints. We improve the lower bound for 18 graphs of standard benchmark DIMACS, and prove the optimal value for 4 graphs by reaching their known upper bound.

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