A parallel lagrangian heuristic for the fractional chromatic number of a graph.

We propose a new integer programming formulation for the Fractional Chromatic Number Problem. The formulation is based on representatives of stable sets. In addition, we present a Lagrangian heuristic from a Lagrangian relaxation of this formulation to obtain a good feasible solution for the problem. Computational experiments are presented to evaluate and compare the upper and lower bounds provided by our approach.