add method is_vertex_cut to (di)graphs

[dcoudert]

This PR answers a query from https://ask.sagemath.org/question/78391/does-sage-have-a-function-to-determine-vertex-cuts/

It adds to (di)graphs a method to check if a set of vertices is a vertex cut of the (di)graph, that is if its removal from the (di)graph increases the number of (strongly) connected components. This generalizes method is_cut_vertex.

📝 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.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit 361ec53; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[lichengzhang1]

For edge versions, a similar problem involves adding a method is_edge_cut to (di)graphs.

[dcoudert]

For edge versions, a similar problem involves adding a method is_edge_cut to (di)graphs.

Sure, but this should be done in another PR. This one is large enough.

[dcoudert]

@fchapoton I need some help here to rebase this branch. I tried to rebase on develop and fix merge conflicts, but push was rejected

MAC-04017247:sage dcoudert$ git push origin HEAD:"graphs/is_vertex_cut"
To https://github.com/dcoudert/sage.git
 ! [rejected]                HEAD -> graphs/is_vertex_cut (non-fast-forward)
error: failed to push some refs to 'https://github.com/dcoudert/sage.git'
hint: Updates were rejected because a pushed branch tip is behind its remote
hint: counterpart. Check out this branch and integrate the remote changes
hint: (e.g. 'git pull ...') before pushing again.
hint: See the 'Note about fast-forwards' in 'git push --help' for details.

[fchapoton]

say "thank you" to the recent doc patch-bombe..

I am not sure how to handle that properly ; my only safe strategy is the following :

did you try to click on the "resolve conflicts" button here and fix the conflicts online ?

[fchapoton]

• are you sure you have the latest develop ?
• you can use "git push -f" to force the push, but be cautious..

[fchapoton]

il y a des instructions precises quand on clique sur "use the command line"

[dcoudert]

• I can't click on "resolve conflicts". It says that "These conflicts are too complex to resolve in the web editor"
• I have the last develop branch (according my clone on GitHub, and git pull)
• I don't see any "use the command line" button
• I will try a forced push...

[dcoudert]

Thanks @fchapoton, the forced push seems ok.

[dcoudert]

something went wrong with my last commit, trying to fix a merge conflict with 10.5.beta4.... I'm not sure how to fix that.
Any advice is more than welcome.

[fchapoton]

well, github requires that the branch is rebased on top of the latest develop. If you merge instead, you git these hundreds of commits..

[fchapoton]

more precisely the commit message must look like
```Merge branch 'develop' into my_cool_branch``

[dcoudert]

I have restarted a branch on top of 10.5.beta4 with a forced push. It should be ok now.

[kwankyu]

    :meth:`is_cut_vertex` | Check whether the input vertex is a cut-vertex.
    :meth:`is_vertex_cut` | Check whether the input vertices form a vertex cut.

This is confusing to me. So is_vertex_cut(G, [v]) does the same with is_cut_vertex(G, v)?

[kwankyu]

"cut vertex" seems a precise term, but "vertex cut" seems not. Do you agree?

[dcoudert]

1. Yes, is_vertex_cut(G, [v]) does the same than is_cut_vertex(G, v).
2. A set of edges whose removal from the graph increases the number of connected components is called a edge cut of the graph. Similarly, a set of vertices whose removal from the graph increases the number of connected components is called a vertex cut. So the terminology used here is the right one. When you refer to a cut vertex v, you refer to a single vertex whose removal increases the number of connected components.

Now, we can ask if method is_cut_vertex is still needed when we have the more general method is_vertex_cut, and knowing that method is_cut_vertex simply calls method is_vertex_cut. The same question holds for methods is_cut_edge and is_edge_cut.

[kwankyu]

OK. Thanks. Reasonable.

[kwankyu]

LGTM.

[kwankyu]

I will wait for ci checks.

[dcoudert]

The error reported by CI in sage -t --long --random-seed=286735480429121101562228604801325644303 src/sage/schemes/elliptic_curves/hom_frobenius.py seems unrelated to changes done in this PR

[kwankyu]

OK. Sorry that this PR got out of my radar.

[dcoudert]

Thank you for the review.