A branch-and-cut algorithm for the equitable coloring problem using a formulation by representatives

Authors:
Laura Bahiense;Yuri Frota;Thiago F. Noronha;Celso C. Ribeiro
Affiliations:
Universidade Federal do Rio de Janeiro, COPPE, Programa de Engenharia de Produção, Rio de Janeiro, RJ 21945-970, Brazil;Universidade Federal Fluminense, Departamento de Ciência da Computação, Niterói, RJ 22410-240, Brazil;Universidade Federal de Minas Gerais, Departamento de Ciência da Computação, Belo Horizonte, MG 31270-010, Brazil;Universidade Federal Fluminense, Departamento de Ciência da Computação, Niterói, RJ 22410-240, Brazil
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

An equitable k-coloring of a graph is defined by a partition of its vertices into k disjoint stable subsets, such that the difference between the cardinalities of any two subsets is at most one. The equitable coloring problem consists of finding the minimum value of k such that a given graph can be equitably k-colored. We present two new integer programming formulations based on representatives for the equitable coloring problem. We propose a primal constructive heuristic, branching strategies, and the first branch-and-cut algorithm in the literature of the equitable coloring problem. The computational experiments were carried out on randomly generated graphs, DIMACS graphs, and other graphs from the literature.