Steps To Reproduce

The following code returns produces a path on 26 vertices:

G = DiGraph( ((x,y) for x,y in Tuples(range(10,100),2) if x!=y and y%sum(ZZ(x).digits())==0), format='list_of_edges' )
with seed(0):
    L = G.longest_path(algorithm='backtrack')
print(L.order())

while G.longest_path(solver='gurobi') produces a path on 64 vertices .

Also, G.longest_path(algorithm='backtrack') ignores the starting vertex when its given. For example, using L = G.longest_path(94, algorithm='backtrack') still produces a path starting at vertex 47.

Expected Behavior

Using algorithm='backtrack' should produce a correct longest path, and obey other given parameters (such as a starting vertex).

Actual Behavior

See above.

Additional Information

No response

Environment

- **OS**: Ubuntu 22.04.3 LTS
- **Sage Version**: 10.2.beta5

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide