A Hamiltonian path on a directed graph G = (V, E) is a path that visits each vertex in V
A Hamiltonian path on a directed graph G = (V, E) is a path that visits each vertex in V
exactly once. Consider the following variants on Hamiltonian path:
(a) Give a polynomial-time
contains either a cycle or a Hamiltonian path (or both). Given a directed graph G,
your algorithm should return true when a cycle or a Hamiltonian path or both and
returns false otherwise.
(b) Show that it is NP-hard to decide whether a directed graph G’ contains both a
cycle and a Hamiltonian Path, by giving a reduction from the HAMILTONIAN
PATH problem: given a graph G, decide whether it has a Hamiltonian path.
(Recall that the HAMILTONIAN PATH problem is NP-complete.)
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