Abstract
Bertossi and Bonuccelli (1986) proved that the Hamiltonian Circuit Problem is NP-complete even when the inputs are restricted to the special class of undirected path graphs. The corresponding problem on directed path graphs was left as an open problem. We use a characterization of directed path graphs due to Monma and Wei (1986) to prove that the Hamiltonian Circuit Problem and the Hamiltonian Path Problem are NP-complete on directed path graphs.
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