A hamiltonian path is a path that contains each vertex of the graph or digraph.
A hamiltonian path is also a hamiltonian cycle,
or hamiltonian circuit,
if the edge vn→v0 exists.
A hamiltonian graph has at least one hamiltonian cycle.
For example, the graph containing two triangles and a connecting edge has a hamiltonian path, but no hamiltonian cycle.
Finding a hamiltonian path, or cycle, is
np complete.