This can be shown by a reduction from the Hamiltonian path problem.

This argument also gives an algorithm for finding the Hamiltonian path.

This doesn't change the shortest Hamiltonian path, but makes sure that it is unique.

The problem of finding Hamiltonian paths in highly symmetric graphs is quite old.

He proved that every finite tournament contains an odd number of Hamiltonian paths.

The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory.

Hamiltonian path - a path that visits each vertex exactly once.

Equivalently, this algorithm finds a Hamiltonian path in the permutohedron.

Such Hamiltonian paths and cycles are also closely connected to Gray codes.

A graph that contains a Hamiltonian path is called a traceable graph.

A simple path that includes every vertex of the graph is known as a Hamiltonian path.

T has exactly one Hamiltonian path.

One proof of this hardness result uses a reduction from the Hamiltonian path problem in directed graphs.

Every finite connected vertex-transitive graph contains a Hamiltonian path.

Note, however, that unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time.

The circular Hamiltonian path for three disks is:

Every hypohamiltonian graph must be 3-vertex-connected, as the removal of any two vertices leaves a Hamiltonian path, which is connected.

It is the only Archimedean dual which does not have a Hamiltonian path among its vertices.

A Hamiltonian path on the knight's tour graph is a knight's tour.

The problem of finding a Hamiltonian path is NP-complete.

There is a simple relation between the problems of finding a Hamiltonian path and a Hamiltonian cycle.

He also introduced the icosian game or Hamilton's puzzle which can be solved using the concept of a Hamiltonian path.

Every Fibonacci cube has a Hamiltonian path.

The requirement of returning to the starting city does not change the computational complexity of the problem, see Hamiltonian path problem.

Additionally, a Hamiltonian path exists between two vertices u,v if and only if have different colors in a 2-coloring of the graph.