1/ What algorithm would you use to count all the hamiltionian paths in a n x m grid graph (n and m <10) from a given starting vertice to an ending one
2/ if this grid graph have holes?
Thanks in advance
Here is Mathematica code that finds all the Hamiltonian paths between opposite corners of a $5 \times 5$ grid graph:
Addendum. Setting $n=7$ to compute the comparable number for a $7 \times 7$ grid returns 223,424 Hamiltonian paths between opposite corners. [5 hrs computation time on a 2.5GHz laptop.] The first one returned is: