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 the 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. 
Tomomi Matsui, Noriyoshi Sukegawa, Atsushi Miyauchi
cs.DS