Lower Bound for (Sum) Coloring Problem

September 19, 2019 · The Ethereal · 🏛 arXiv.org

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Authors Alexandre Gondran, Vincent Duchamp, Laurent Moalic arXiv ID 1909.08906 Category cs.DM: Discrete Mathematics Cross-listed cs.RO Citations 0 Venue arXiv.org Last Checked 5 months ago
Abstract
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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