The traveling salesman problem for cubic graphs
<|reference_start|>The traveling salesman problem for cubic graphs: We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2^{n/3}) ~= 1.260^n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound. We can also count or list all Hamiltonian cycles in a degree three graph in time O(2^{3n/8}) ~= 1.297^n. We also solve the traveling salesman problem in graphs of degree at most four, by randomized and deterministic algorithms with runtime O((27/4)^{n/3}) ~= 1.890^n and O((27/4+epsilon)^{n/3}) respectively. Our algorithms allow the input to specify a set of forced edges which must be part of any generated cycle. Our cycle listing algorithm shows that every degree three graph has O(2^{3n/8}) Hamiltonian cycles; we also exhibit a family of graphs with 2^{n/3} Hamiltonian cycles per graph.<|reference_end|>
@article{eppstein2003the,
    title={The traveling salesman problem for cubic graphs},
    author={David Eppstein},
    journal={J. Graph Algorithms and Applications 11(1):61-81, 2007},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0302030},
    primaryClass={cs.DS}
}