Is the Hamiltonian Cycle an NP Problem?

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In summary, the conversation discusses the topic of the Hamiltonian cycle problem in graph theory and whether it is considered an NP problem. It is mentioned that the problem is NP-complete and there is no question about this fact. One individual also mentions having an algorithm for the problem, but it is not clear if this would solve the NP=P problem.
  • #1
neurocomp2003
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sup, just realized there is not graphtheory/combinatorial subforums.

is the hamiltonian cycle still considered and NP problem?
 
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  • #2
The problem of finding a Hamiltonian cycle in a graph is NP-complete (and therefore NP). This is a proven fact; it is not something that is under consideration (and so it will not change in the future).
 
  • #3
I wonder what thought could have raised this question :)

-- AI
 
  • #4
having an algorithm that i want to code but I'm lazy. and if the question of NP=P was solved then there was no point =] guess that should have been my question but I just wanted to see if there was apaper out their that said H=P.
 
  • #5
As master_coda has stated, Hamiltonian is "proved" to be NP-complete.
Now, if i understand your last post, then you seem to have an algorithm for Hamiltonian in which case you have solved the NP=P problem! When are we going to see your paper coming out :D

-- AI
 
  • #6
hahah i have an algorithm that I would like to try and see if it goes anywhere...not going to say it'll solve NP=P, but i want to see if it can go somewhere.
 

1. What is a Hamiltonian?

A Hamiltonian is a mathematical function that describes the total energy of a system. It is used in physics and engineering to model and analyze the behavior of dynamic systems. In computer science, the term Hamiltonian is often used in relation to the complexity class NP.

2. What does it mean for a Hamiltonian to be NP?

In computational complexity theory, NP (nondeterministic polynomial time) is a class of decision problems that can be solved by a nondeterministic Turing machine in polynomial time. A Hamiltonian being in NP means that there exists a polynomial-time algorithm to solve the problem of finding a Hamiltonian cycle in a graph.

3. Is Hamiltonian still NP-complete?

No, it is not. In the 1970s, it was proven that the problem of finding a Hamiltonian cycle in a graph is NP-complete. However, in 2002, it was shown that the Hamiltonian path problem is NP-complete, but the Hamiltonian cycle problem is not. This means that the problem of determining whether a graph has a Hamiltonian cycle is in the complexity class NP, but it is not NP-complete.

4. Can Hamiltonian still be solved in polynomial time?

It is not known whether the Hamiltonian cycle problem can be solved in polynomial time. It is an open problem in computer science and mathematics. Some researchers believe that there is no polynomial-time algorithm for this problem, while others believe that there may be a more efficient algorithm yet to be discovered.

5. Why is the question "Is Hamiltonian still NP?" important?

The question is important because the complexity class NP is a fundamental concept in computer science and mathematical theory. Understanding the complexity of the Hamiltonian cycle problem can provide insights into the complexity of other problems in NP and help researchers develop more efficient algorithms for solving them. It also has practical applications in areas such as network optimization and logistics planning.

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