Polyhedral results for the Equitable Coloring Problem
Isabel M\'endez-D\'iaz, Graciela Nasini, Daniel Severin
TL;DR
This paper investigates the polyhedral structure of the Equitable Coloring Problem, identifying new valid inequalities and facet conditions, and demonstrates their effectiveness in improving a Branch & Cut algorithm through computational experiments.
Contribution
It introduces new families of valid inequalities and facet-defining conditions for the polytope related to the Equitable Coloring Problem, enhancing solution methods.
Findings
New valid inequalities improve cutting-plane methods.
Facet conditions help identify strong inequalities.
Computational results show improved algorithm performance.
Abstract
In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence of the effectiveness of including these inequalities as cuts in a Branch & Cut algorithm.
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