Questions tagged [hamiltonian-path]

Questions on Hamiltonian paths, that is, paths that visit each vertex exactly once in a graph.

12 questions with no upvoted or accepted answers
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How can the shortest traveling salesman tour be found in $O(2^n poly(n))$ time and less than exponential space?

I'm stuck on problem 9.4 from The Nature of Computation which reads: Dynamic Salesman. A naive search algorithm for TSP takes $O(n!)$ time to check all tours. Use dynamic programming to reduce this ...
5
votes
0answers
184 views

Upper bound on the number of hamiltonian cycles on a $n \times n $ grid graph

What is the best upper bound that is known for the number of hamiltonian cycles on a $n \times n $ grid graph? I did some searching and found that the number of hamiltonian cycles on a planar graph ...
3
votes
0answers
357 views

Finding partial traveling salesman path of specified length

For a given set of nodes, I can find optimal paths that visit all nodes using various traveling salesman algorithms. As a subset of this problem, I would like to be able to find shortest partial ...
3
votes
1answer
298 views

Number of “hamiltonian tours” from upper left to lower left corner of a grid graph?

I got the following as an interview question: Count the number of tours from the upper left corner to the lower left corner in a grid world where you can move in any manhattan direction. This is the ...
2
votes
0answers
2k views

Prove that a hamiltonian DAG has a single topological sort

I've been straggling a little proving the argument "a hamiltonian directed acyclic graph has a single topological sort". This is pretty much the idea of what I've come along: lets prove by ...
1
vote
0answers
453 views

Minimum weight Hamiltonian path on a weighted (0 and 1) tournament graph

Suppose we have a weighted tournament graph. (A directed graph in which every pair of distinct vertices is connected by a single directed edge.) The weights are constrained to be 0 and 1. I know ...
1
vote
0answers
2k views

Poly-time reduction from directed Hamiltonian Path to undirected HP, both with with known start and end

this is homework, so PLEASE do not give me the solution(!), but help me get there on my own. I've got to proof that directed Hamilton Path with fixed stard and ending and undirected Hamilton Path ...
0
votes
0answers
45 views

Why do you need 3 intermediate nodes when reducing a directed hamiltonian path to undirected?

To prove that the undirected hamiltonian path problem is NP-complete, I have to reduce it from the directed hamiltonian path. Sipser encodes each intermediate node from node ...
0
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0answers
28 views

Number of Hamilton paths in graphs

I am trying to find a fast algorithm that can compute the number of hamiltonian paths in an undirected graph. I saw this on the web, but it sounds like this finds all hamiltonian paths starting from ...
0
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0answers
21 views

Does this imply Hamiltonian path cannot be decided in nondeterministic logspace?

Suppose I nondeterministically walk around in a graph with n vertices. When looking for a Hamiltonian path, at some point I’ve walked n/2 vertices. There are (n choose n/2) different combinations of ...
0
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0answers
36 views

Does this imply checking a candidate Hamiltonian Path solution can be done in logspace?

Assume vertices are integers base 2. Smallest vertex is 1. There are n vertices. Our input is: the number of vertices (n expressed in log(n) bits - ...
0
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0answers
39 views

Non intersecting paths of graphs with obstacle number one

There are $N$ points inside a polygon. If two points are connected by an edge (a line segment) if the edge is completely inside the polygon. We could conclude finding a Hamiltonian path is NPC, but ...