Strengthened Entire Programming Formulation for the Grundy Color Problem

The Grundy Coloring Problem consists in determining the largest number of cores produced by a rough coloring of a graph. In this work, we propose preparations for an integral programming formulation based on asymmetrical representatives. As contributions include the use of the order \emph{Smallest-Last} (SL) to define the relation of representation of the model, in addition to new valid inequalities associated with the variations of order of the classes of core and the strengthening of the restrictions of the Miller--Tucker--Zemlin (MTZ) type. Computational experiments indicate that the strengthened formulations significantly reduce the number of nodes explored and the resolution time, especially in sparse and moderately dense graphs.