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Lower Bound for (Sum) Coloring Problem

Discrete Mathematics 2019-09-20 v1 Robotics

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.

Keywords

Cite

@article{arxiv.1909.08906,
  title  = {Lower Bound for (Sum) Coloring Problem},
  author = {Alexandre Gondran and Vincent Duchamp and Laurent Moalic},
  journal= {arXiv preprint arXiv:1909.08906},
  year   = {2019}
}