A polyhedral approach to edge coloring

We formulate the edge coloring problem on a simple graph as the integer program of covering edges by matchings. For the NP-hard case of 3-regular graphs we show that it is sufficient to solve the linear programming relaxation with the additional constraints that each odd circuit be covered by at least three matchings. We give an efficient separation algorithm for recognizing violated odd circuit constraints and a linear programming based constrained weighted matching algorithm for pricing. Computational experiments with the overall linear programming system are presented.