On the asymmetric representatives formulation for the vertex coloring problem

We consider the vertex coloring problem, which may be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each vertex receives at least one label and the endpoints of all edges are assigned different labels. In this work, the 0-1 integer programming formulation based on representative vertices is revisited to remove symmetry. The previous polyhedral study related to original formulation is adapted and generalized. New versions of facets derived from substructures of G are presented, including cliques and odd holes, antiholes and wheels. In addition, a new class of facets is derived from independent sets of G. Finally, a comparison with the independent sets formulation is provided.

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Manoel B. Campêlo, Victor A. Campos, Ricardo C. Corrêa
• Keywords: DAM 2008, Independent Sets, Labels, Vertex Coloring Problem