Question: Assume that the Hamiltonian cycle problem is NP-complete for undirected graphs. a. Prove that the Hamiltonian cycle problem is NP-complete for directed graphs. b. Prove

Assume that the Hamiltonian cycle problem is NP-complete for undirected graphs.
a. Prove that the Hamiltonian cycle problem is NP-complete for directed graphs.
b. Prove that the unweighted simple longest-path problem is NP-complete for directed graphs.

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