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}
}