On the asymmetric representatives formulation for the vertex coloring problem 1 Manoel Campˆ elo a,2 , Victor Campos a,3 , Ricardo Corrˆ ea a,4 a Mestrado e Doutorado em Ciˆ encia da Computa¸c˜ ao Universidade Federal do Cear´ a Fortaleza-CE, Brazil Abstract The representatives formulation for the vertex coloring problem is revisited to re- move symmetry and new versions of facets derived from substructures of the graph are presented. In addition, a new class of facets is derived from independent sets of the graph. Finally, a comparison with the independent sets formulation is provided. Keywords: facets of polyhedra, graph coloring, integer programming 1 Introduction A coloring of a graph G is an assignment of colors to its vertices so that each vertex receives at least one color and the endpoints of all edges are assigned different colors. The vertex coloring problem is defined as the minimization of the number of colors χ(G) that must be used in a coloring of G. 1 All authors are partially supported by the Conselho Nacional de Desenvolvimento Cient´ ıfico e Tecnol´ogico, CNPq, Brazil. 2 Email: mcampelo@lia.ufc.br 3 Email: campos@lia.ufc.br 4 Email: correa@lia.ufc.br Electronic Notes in Discrete Mathematics 19 (2005) 337–343 1571-0653/2005 Published by Elsevier B.V. www.elsevier.com/locate/endm doi:10.1016/j.endm.2005.05.045