Questions tagged [hamiltonian-paths]

A path in a graph is said to be Hamiltonian if it visits each vertex exactly once.

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4answers
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List of strongly NP-hard problems with numerical data

I am looking for strongly NP-hard problems for a reduction. So far I have found the following problems: 3-partition problem bin-packing problem Numerical 3-dimensional matching TSP Any NP-complete ...
25
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2answers
3k views

Hamiltonicity of k-regular graphs

It is known that it is NP-complete to test whether a Hamiltonian cycle exists in a 3-regular graph, even if it is planar (Garey, Johnson, and Tarjan, SIAM J. Comput. 1976) or bipartite (Akiyama, ...
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1answer
3k views

Is the longest trail problem easier than the longest path problem?

The longest path problem is NP-hard. The (typical?) proof relies on a reduction of the Hamiltonian path problem (which is NP-complete). Note that here the path is taken to be (node-)simple. That is, ...
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3answers
281 views

Problems with Unknown Single Exponential Time Agorithms

I'm looking for examples of problems for which it is easy to get algorithms running in time $2^{O(n\log n)}$, or $2^{O(n^c)}$ for some $c>1$ but for which it is not known whether there is an ...
6
votes
1answer
539 views

Two Hamiltonian path problem variants

While formalizing the gadgets for the proposed reduction of the question Efficient algorithm for existence of permutation with differences sequence? the following problems came to my mind: Problem 1 ...
2
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1answer
160 views

Is balanced Hamiltonian cycle NP complete on maximal plane graphs?

I know that the Hamiltonian cycle is NP complete on the class of maximal plane graphs. If we instead ask about balanced Hamiltonian cycles (i.e. same number of faces on both sides) on maximal plane ...
2
votes
1answer
232 views

Searching for name of equivalence property in hamiltonian paths

This one has been bugging me for a while. A long time ago in undergrad, I noticed this while learning about TSP. Nobody recognized it and I basically gave up. Given a hamiltonian path, any subpath ...
2
votes
3answers
957 views

Best bounds for the longest path optimization problem in cubic Hamiltonian graph?

optimization problem Input: cubic Hamiltonian graph feasible solution: A simple path measure to optimize: length of the simple path Design a polynomial-time algorithm that outputs the longest path ...
7
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2answers
413 views

On the class of the FNP version of the Hamiltonian Cycle problem

This post is linked to: FNP complexity class Many places say that the decision version of Hamiltonian Cycle is NP-Complete, and NP-Complete problems are those whose solution can be verified in ...
4
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3answers
517 views

FNP complexity class

Where can I find more information about the FNP complexity class? The only place I did find anything on FNP was http://en.wikipedia.org/wiki/FNP_(complexity) However, that isn't sufficient for me to ...
3
votes
2answers
414 views

Hamiltonian cycle on a subset of 2D points, constrained by maximum total length

We are given a list of 2d coordinates, each coordinate representing a node in a graph, and a scalar D, which is a constraint on total length of the cycle. The task is to find a Hamiltonian cycle on a ...
3
votes
2answers
341 views

Complexity of the Hamiltonian Subcycle problem

The problem is as follows: Given a graph $G$, find a (vertex) disjoint set of cycles $C$ on $G$ such that every vertex is visited by a cycle exactly once. My question is then: what is the ...