  The three domatic number problem asks whether a given undirected graph can be
partitioned into at least three dominating sets, i.e., sets whose closed
neighborhood equals the vertex set of the graph. Since this problem is
NP-complete, no polynomial-time algorithm is known for it. The naive
deterministic algorithm for this problem runs in time 3^n, up to polynomial
factors. In this paper, we design an exact deterministic algorithm for this
problem running in time 2.9416^n. Thus, our algorithm can handle problem
instances of larger size than the naive algorithm in the same amount of time.
We also present another deterministic and a randomized algorithm for this
problem that both have an even better performance for graphs with small maximum
degree.
