Mercedes Landete and José Luis Sainz-Pardo (Operations Research Center, University Miguel Hernández of Elche)
Abstract: The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating sets. Both problems were proved to be NP-complete. In this paper, we present a decomposition algorithm for finding a domatic partition on separable graphs, that is, on graphs with blocks, and as a consequence, its domatic number, highly reducing the computational complexity. Computational results illustrate the benefits of the block decomposition algorithm.