Can the Hamiltonian cycle problem be solved in polynomial time?

No solution exists to get HC in polynomial time and there are no such conditions to decide the probability of HC exists (Neapolitan and Naimipour, 1996).

How do you prove that the Hamiltonian cycle is NP-complete?

The number of calls to the Hamiltonian path algorithm is equal to the number of edges in the original graph with the second reduction. Hence the NP-complete problem Hamiltonian cycle can be reduced to Hamiltonian path, so Hamiltonian path is itself NP-complete.

When Hamiltonian cycle is not possible?

the number of vertices is odd then no Hamilton cycle is possible. if it’s not 2-connected , simply check out the literature on the travelling salesman problem, there are probably already tons of cuts (for the corresponding IP-formulation) developed for that problem.

In what time can the Hamiltonian path problem can be solved using dynamic programming?

7. In what time can the Hamiltonian path problem can be solved using dynamic programming? Explanation: Using dynamic programming, the time taken to solve the Hamiltonian path problem is mathematically found to be O(N2 2N).

Is Hamiltonian cycle polynomial time?

Definition: A Hamiltonian cycle is a cycle in a graph that visits each vertex exactly once. It takes time proportional to n, because there are n vertices to count and n edges to check. n is a polynomial, so the check runs in polynomial time. Therefore, Hamiltonian Cycle E NP.

Is Hamiltonian cycle in P?

Yes. Hamiltonian cycle is a NP-complete problem.

How do you prove no Hamiltonian cycle?

Proving a graph has no Hamiltonian cycle [closed]

1. A graph with a vertex of degree one cannot have a Hamilton circuit.
2. Moreover, if a vertex in the graph has degree two, then both edges that are incident with this vertex must be part of any Hamilton circuit.
3. A Hamilton circuit cannot contain a smaller circuit within it.

Which of the following algorithms can be used to solve the Hamiltonian Path Problem efficiently?

Explanation: the hamiltonian path problem can be solved efficiently using branch and bound approach. it can also be solved using a backtracking approach.

How many times do you visit a vertex when traveling either a Hamilton circuit or path?

Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex. Hamiltonian circuits are named for William Rowan Hamilton who studied them in the 1800’s.

Is Hamiltonian cycle NP-complete?

Therefore, any instance of the Hamiltonian Cycle problem can be reduced to an instance of the Hamiltonian Path problem. Thus, the Hamiltonian Cycle is NP-Hard. Conclusion: Since, the Hamiltonian Cycle is both, a NP-Problem and NP-Hard. Therefore, it is a NP-Complete problem.