Hamiltonian cycle problem
The Hamiltonian cycle or Hamiltonian circuit problem in graph theory is to find a path through a given graph which starts and ends at the same vertex and includes each vertex exactly once.
It is a special case of the traveling salesman problem, obtained by setting the distance between two cities to unity if they are adjacent and infinity otherwise. Like the traveling salesman problem, the Hamiltonian cycle problem is NP-complete.
The requirement that the path start and end at the same vertex distinguishes it from the Hamiltonian path problem.
The problem is named after Sir William Rowan Hamilton.
See also: Hamiltonian path
