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- Show that an algorithm that makes at most a constant number of
calls to polynomial-time subroutines runs in polynomial time, but that a
polynomial number of calls to polynomial-time subroutines may result in an
- A Hamiltonian path in a graph is a simple path that visits every
vertex exactly once. Show that the decision problem of determining
whether or not there is a Hamiltonian path from a given vertex u to
another given vertex v belongs to NP
- Show that the
relation is a transitive relation on the
set of problems.
- Given an undirected graph, the Hamiltonian cycle
problem determines whether a graph has a Hamiltonian cycle.
Given that the Hamiltonian cycle problem for
undirected graphs is NP-Complete, what can you say about the
Hamiltonian cycle problem for directed graphs? Provide
reasons for your answer.