adding has_subgraph_decomposition method to GenericGraph

[seblabbe]

Following the question https://ask.sagemath.org/question/81610/test-if-a-graph-has-a-claw-decomposition/,
the current PR is adding a has_subgraph_decomposition method to the GenericGraph class.

It also adds a _subgraph_decomposition_dlx method allowing to enumerate/count the decompositions.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

[seblabbe]

A question I still have is whether a method has_subgraph_decomposition is the best choice. Should it rather be a method subgraph_decomposition returning a decomposition? Should it be a method subgraph_decompositions returning an iterator over all decomposition?

[seblabbe]

While I was writing the code, I observed a bug in the current subgraph search which yield duplicate copies of the same subgraph. This is why I first need to create a set of rows to avoid duplicates.

I created #39599 for this issue.

[github-actions]

Documentation preview for this PR (built with commit 40cbaf3; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[dcoudert]

Some comments

• It seems that the method is currently for undirected graphs only. If so, it should be in graph.py or in a new module devoted to subgraph search and subgraph partition/covering.
• I like the idea of an iterator subgraph_decompositions.
• I don't see the need for method _subgraph_decomposition_dlx. Unless you plan to implement several methods, it can be included in the main method.
• Concerning subgraph_search_iterator, I don't know how to avoid returning several times the same graph. If you have an algorithm in mind, we could at its implementation to the list of GSoC'25 project proposals.
• Add a warning in the method that the memory consumption can be huge, and a todo statement to recall to improve the implementation when subgraph_search_iterator will be improved

[dcoudert]

remove empty line

[dcoudert]

edge_to_column_id = {frozenset(edge): i for I, edge in enumerate(edges)}

[dcoudert]

add path in sagemath

[dcoudert]

remove empty line.

may be add some tests when the method is not working ? what if the graph is not simple ?

[dcoudert]

if not certificate:
    return has_solution
if has_solution:
    return has_solution, F(solution)
return has_solution, solution