New Results on the Queens n2 Graph Coloring Problem

Michel Vasquez (1)

1 LGI2P - Laboratoire de Génie Informatique et Ingénierie de Production

For the Queens_n 2 graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.

Mots clés: queens graphs; graph coloring; independent sets; cliques based filtering

Domaines: Recherche opérationnelle [math.OC]

Michel Vasquez. New Results on the Queens n2 Graph Coloring Problem. Journal of Heuristics, 2004, 10 (4), pp.407-413. ⟨10.1023/B:HEUR.0000034713.28244.e1⟩. ⟨hal-00353835⟩