Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian path that is a cycle. Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem.
One possible Hamiltonian cycle through every vertex of a dodecahedron is shown in red – like all platonic solids, the dodecahedron is Hamiltonian.
Generate all possible configurations of vertices and print a
configuration that satisfies the given constraints. There
will be n! (n factorial) configurations.
while there are untried configurations
{
generate the next configuration
if ( there are edges between two consecutive vertices of this
configuration and there is an edge from the last vertex to
the first ).
{
print this configuration;
break;
}
}
Create an empty path array and add vertex 0 to it. Add other
vertices, starting from the vertex 1. Before adding a vertex,
check for whether it is adjacent to the previously added vertex
and not already added. If we find such a vertex, we add the
vertex as part of the solution. If we do not find a vertex
then we return false.