Why Is Longest Path Np Complete?

Now it is easy to conclude that Longest Path is NP-complete because it is in NP and HamiltonianPath ∝ LongestP ath simply by observing that there is a Hamiltonian path in G if and only if there is a path of length n − 1.

Is path finding NP-complete?

In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative-weight cycles, the longest path problem is NP-hard and the decision version of the problem, which asks whether a path exists of at least some given length, is NP-complete.

Why is path not NP-complete?

Hence, the only way to prove that PATH is not NP-complete is proving that there is at least one NP problem that cannot be reduced to PATH in polynomial time. Unfortunately, you will find that this depends on the P vs NP open problem.