1 | initial version |
Hi,
Sage has the command:
hamiltonian_cycle(algorithm='tsp')
"Returns a Hamiltonian cycle/circuit of the current graph/digraph A graph (resp. digraph) is said to be Hamiltonian if it contains as a subgraph a cycle (resp. a circuit) going through all the >vertices. Computing a Hamiltonian cycle/circuit being NP-Complete, this algorithm could run for some time depending on the instance.
ALGORITHM:
See Graph.traveling_salesman_problem for ‘tsp’ algorithm and find_hamiltonian from sage.graphs.generic_graph_pyx for >>‘backtrack’ algorithm.
INPUT:
algorithm - one of ‘tsp’ or ‘backtrack’. OUTPUT: If using the ‘tsp’ algorithm, returns a Hamiltonian cycle/circuit if it exists; otherwise, raises a EmptySetError exception. If >>using the ‘backtrack’ algorithm, returns a pair (B,P). If B is True then P is a Hamiltonian cycle and if B is False, P is a >>longest path found by the algorithm. Observe that if B is False, the graph may still be Hamiltonian. The ‘backtrack’ >>algorithm is only implemented for undirected graphs."
The above is directly from Hamiltonian Cycle
Added in the same area on the page is:
sage: g = graphs.HeawoodGraph()
sage: g.hamiltonian_cycle()
TSP from Heawood graph: Graph on 14 vertices
sage: g = graphs.PetersenGraph()
sage: g.hamiltonian_cycle()
Traceback (most recent call last):
...
EmptySetError: The given graph is not Hamiltonian
So clearly there is some algorithms on your question, though it is also known that this is an NP-Complete problem.
Good luck, fieldofnodes