An Exact 29416^n Algorithm for the Three Domatic Number Problem
<|reference_start|>An Exact 29416^n Algorithm for the Three Domatic Number Problem: 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.<|reference_end|>
@article{riege2005an,
    title={An Exact 2.9416^n Algorithm for the Three Domatic Number Problem},
    author={Tobias Riege, J"org Rothe},
    journal={arXiv preprint arXiv:cs/0506090},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0506090},
    primaryClass={cs.CC}
}