Complexity of generalized graph coloring

We characterize the complexity of the class of generalized coloring problems, denoted GCP F,k , which arise in resource allocation and VLSI theory. Depending on the parameters, this complexity ranges from polynomial to ∑ 2 p -complete. The latter represent apparenly the first natural graph problems to be complete for any intermediate slot of the polynomial hyerarchy. A parallelizable algorithm for the polynomial problems is presented.