Rule 1:
If a vertex v has degree 2, then both of its incident edges must be part of any Hamiltonian cycle.
Rule 2:
During the construction of a Hamiltonian cycle, no cycle can be formed until all vertices have been visited.
Rule 3:
If during the construction of a Hamiltonian cycle two of the edges incident on a vertex v are shown to be required, then all other incident edges can be deleted.
(Gross & Yellen, 1999)
