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.
The source code is available on GitHub. Be aware that this is a work-in-progress, and the code is at a very early stage.

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