A DSATUR-based algorithm for the Equitable Coloring Problem

This paper describes a new exact algorithm for the Equitable Coloring Problem, a coloring problem where the sizes of two arbitrary color classes differ in at most one unit. Based on the well known DSatur algorithm for the classic Coloring Problem, a pruning criterion arising from equity constraints is proposed and analyzed. The good performance of the algorithm is shown through computational experiments over random and benchmark instances.Fil: Méndez-Díaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

Grundy dominating sequences on X-join product

In this paper we study the Grundy domination number on the X-join product G↩R of a graph G and a family of graphs R={Gv:v∈V(G)}. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all v∈V(G), the Grundy domination number of Gv is given, and G is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of G↩R can be done in polynomial time. In particular, our results for powers of cycles and paths are derived from a polynomial reduction to the Maximum Weight Independent Set problem on these graphs. As a consequence, we derive closed formulas to compute the Grundy domination number of the lexicographic product G∘H when G is a power of a cycle, a power of a path or a split graph, generalizing the results on cycles and paths given by Brešar et al. in 2016. Moreover, our results on the X-join product when G is a split graph also provide polynomial-time algorithms to compute the Grundy domination number for (q,q−4) graphs, partner limited graphs and extended P4-laden graphs, graph classes that are high in the hierarchy of few P4’s graphs.Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Torres, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin