A column generation approach for graph coloring

The authors 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). They 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 difficult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. The authors have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented.