Lower Bounding Techniques for DSATUR-based Branch and Bound

Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph such that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound is a well-known exact algorithm for the VCP. One of its main drawbacks is that a lower bound (equal to the size of a maximal clique) is computed once at the root of the branching scheme and it is never updated during the execution of the algorithm. In this article, we show how to update the lower bound and we compare the efficiency of several lower bounding techniques.