We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree. This approach, while requiring the solution of a di cult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented.
For instance, Mehrotra and Trick REF present a formulation of the graph coloring problem that avoids color symmetries.
A Column Generation Approach For Graph Coloring
INFORMS Journal on Computing
Computer Science Mathematics