Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once a...

This paper describes a new exact algorithm PASS for the vértex coloring problem based on the well Keywordsknown DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate Color vértex to color, breaking ties by máximum degree w.r.t. uncolored vértices. Later Sewell introduced a Graph new tiebreaking strategy, which evaluated available colors for each vértex expl...

This paper describes an exact algorithm for the Equitable Coloring Problem, based on the well known DSatur algorithm for the classic Coloring Problem with new pruning rules specifically derived from the equity constraint. Computational experiences show that our algorithm is competitive with those known in literature.

Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch and Bound (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once and it is n...

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no ...

In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably with the well-known ex...

Addressing scheduling problems with the best graph coloring algorithm has always been very challenging. However, university timetable problem can be formulated as a where courses are represented vertices and presence of common students or teachers corresponding edges. After that, stands to color lowest possible colors. In order accomplish this task, paper presents comparative study use in sched...