I am interested in the Hamiltonian Cycle problem. I have built some simple tools in Perl, to visualize graphs, and to attempt to solve the Hamiltonian Cycle problem in polynomial time, for a user-entered graph. This is an early prototype of the algorithm, which is a work-in-progress, on its way to becoming a CPAN module.
Here is a relatively complex graph being evaluated by the Hamiltonian Graph Detector. This script often simplifies the input graph by removing vertices and edges, according to certain rules. Also, the Hamiltonian Graph Detector generates isomorphs of the input graph. All transforms are done while preserving the
is_hamiltonian() property.
- Here is another complex graph which the script correctly detects as non-Hamiltonian.
- Here is a simple graph which is obviously Hamiltonian.
- Another complex graph, correctly detected as Hamiltonian.
- Here is the Herschel Graph. The Herschel Graph is richly connected; all vertices have degree 3 or 4. One would intuitively expect the Herschel Graph to be Hamiltonian. However, the Herschel Graph is the smallest, non-Hamiltonian, polyhedral graph.
- Ashwin Dixit
ashwin at ownlifeful dot com