.edge_cut(algorithm='LP') returns edges without labels

[maxale]

Steps To Reproduce

sage: g = graphs.PetersenGraph()

sage: g.edge_cut(0, 3, vertices=True, use_edge_labels=True)
[3,
 [(0, 1, None), (0, 4, None), (0, 5, None)],
 [[0], [1, 2, 3, 4, 5, 6, 7, 8, 9]]]

sage: g.edge_cut(0, 3, vertices=True, use_edge_labels=True, algorithm="FF")
[3,
 [(0, 1, None), (0, 4, None), (0, 5, None)],
 [[0], [1, 2, 3, 4, 5, 6, 7, 8, 9]]]

sage: g.edge_cut(0, 3, vertices=True, use_edge_labels=True, algorithm="LP")
(3, [(2, 3), (3, 4), (3, 8)], [[0, 1, 2, 4, 5, 6, 7, 8, 9], [3]])

Expected Behavior

.edge_cut(algorithm='LP') should return edges with labels, consistently with other algorithms.

Actual Behavior

Edges are reported as tuples of vertices without labels.

Additional Information

It breaks other methods that depend on .edge_cut such as .gomory_hu_tree(algorithm="LP"), which fails with an error:

ValueError: not enough values to unpack (expected 3, got 2)

as reported at https://ask.sagemath.org/question/79320/

Environment

• OS: Ubuntu 24.04.1 LTS
• Sage Version: 10.5.beta3

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

[dcoudert]

I pushed a fix in #38725.