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

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 that the unweighted simple longest-path problem is NP-complete for directed graphs.