Title:   Fractional programming formulation for the vertex coloring problem

We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is fractional, it can be replaced by a piece-wise linear convex function. Numerical experiments show that our formulation has significantly good performance for dense graphs. Based on join work with Tomomi Matsui and Atsushi Miyauchi.