Implemented methods concerning bricks and braces of a matching covered graph #39065

janmenjayap · 2024-12-01T08:07:13Z

The objective of this issue is to implement the methods pertaining to the bricks and brace of a matching covered graph.

More specifically, this PR aims to implement the following two methods:

bricks_and_braces() | Return the list of (underlying simple graph of) the bricks and braces of the (matching covered) graph.
is_brace() | Check if the (matching covered) graph is a brace
is_brick() | Check if the (matching covered) graph is a brick.
number_of_braces() | Return the number of braces.
number_of_bricks() | Return the number of bricks.
number_of_petersen_bricks() | Return the number of Petersen bricks.
tight_cut_decomposition() | Return a tight cut decomposition.

This PR shall address the methods related to bricks, braces and tight cut decomposition of matching covered graphs.

Fixes #38216.
Note that this issue fixes a small part of the mentioned issue.

📝 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

This PR depends on the PR #38742 and #38892.

cc: @dcoudert.

github-actions · 2024-12-01T08:49:02Z

Documentation preview for this PR (built with commit 7455ac0; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

src/sage/graphs/matching_covered_graph.py

dcoudert

Check your code to avoid redundant operations.

src/sage/graphs/matching_covered_graph.py

janmenjayap · 2024-12-01T15:17:53Z

Please note that for the following doctest:

One may set the ``coNP_certificate`` to be ``True``::

            sage: H = graphs.HexahedralGraph()
            sage: G = MatchingCoveredGraph(H)
            sage: G.is_brace(coNP_certificate=True)
            (True, None, None)
            sage: C = graphs.CycleGraph(6)
            sage: D = MatchingCoveredGraph(C)
            sage: D.is_brace(coNP_certificate=True)
            (False, [(0, 5, None), (2, 3, None)], {0, 1, 2})

It is passing in my local for the following two commands:

./sage -t src/sage/graphs/matching_covered_graph.py
./sage -t --long --warn-long 30.0 --random-seed=48323011685507437272567463462221430408 src/sage/graphs/matching_covered_graph.py

However, it is failing in the check for Build & Test / test-new (pull_request).

dcoudert · 2024-12-01T15:30:02Z

is the returned certificate valid ? if so, you must make the method or doctest more robust. This might be a side effect of some data structure (set, graph, etc.) that do not guaranty the order of the items.

janmenjayap · 2024-12-01T15:31:37Z

Yes. Both of the certificates are valid.

…

On Sun, 1 Dec, 2024, 9:00 pm David Coudert, ***@***.***> wrote: is the returned certificate valid ? if so, you must make the method or doctest more robust. This might be a side effect of some data structure (set, graph, etc.) that do not guaranty the order of the items. — Reply to this email directly, view it on GitHub <#39065 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AT2NIZGAEE2UHVDNIZYYH632DMTQ7AVCNFSM6AAAAABSZM5QQGVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKMBZHAYTMOBQGA> . You are receiving this because you authored the thread.Message ID: ***@***.***>

src/sage/graphs/matching_covered_graph.py

user202729 · 2024-12-03T13:11:31Z

Please note that for the following doctest:
One may set the ``coNP_certificate`` to be ``True``::

            sage: H = graphs.HexahedralGraph()
            sage: G = MatchingCoveredGraph(H)
            sage: G.is_brace(coNP_certificate=True)
            (True, None, None)
            sage: C = graphs.CycleGraph(6)
            sage: D = MatchingCoveredGraph(C)
            sage: D.is_brace(coNP_certificate=True)
            (False, [(0, 5, None), (2, 3, None)], {0, 1, 2})
It is passing in my local for the following two commands:

./sage -t src/sage/graphs/matching_covered_graph.py

./sage -t --long --warn-long 30.0 --random-seed=48323011685507437272567463462221430408 src/sage/graphs/matching_covered_graph.py

However, it is failing in the check for Build & Test / test-new (pull_request).

I don't think it's a very large issue. We have # random for that.

You can then do e.g. manual checking that the result is in some finite list in a TESTS:: block later.

Co-authored-by: user202729 <[email protected]>

dcoudert · 2024-12-07T12:17:02Z

You may implement a method to check that the returned certificate is valid and use it instead of printing the certificate.

dcoudert · 2024-12-15T17:52:54Z

src/sage/graphs/matching_covered_graph.py

+            :meth:`~sage.graphs.graph.Graph.is_bicritical`
+        """
+        if self.is_bipartite():
+            raise ValueError('the input graph is bipartite')


why raising an error and not returning False ?

I suppose it's more of that p → q logic statement.
Like given a nonbipartite matching covered graph (statement p), it is a brick if it is free of nontrivial tight cuts (statement q).

The definition includes the term nonbipartite. so if not p (that is either it is bipartite or not matching covered or both), then the statement is always true.

Also, in the case of bipartite if we return False, we don't have any useful coNP certificate. One may avoid this ValueError, just by checking if it is bipartite or not before checking if it is a brick.

I might be wrong. I will be glad to have your view.

Raising an error is not a good behavior here. If the issue is that you don't khave a coNP certificate, then you can return an extra boolean indicating that the input is bipartite.

Good point. That's also I have thought of. But the method is_brick() is solely defined for nonbipartite graphs and in that case, we have to return an extra boolean True showing that the graph is nonbipartite for each valid and useful input instances of the method, which seems a bit unnecessary.

src/sage/graphs/matching_covered_graph.py

… into bricks_and_braces

dcoudert · 2024-12-27T12:11:33Z

src/sage/graphs/matching_covered_graph.py

@@ -2663,6 +3260,14 @@ def remove_loops(self, vertices=None):

        return

+    @doc_index('Bricks, braces and tight cut decomposition')
+    def tight_cut_decomposition(self):


Why are you adding this method in this PR ? It would be better to finalize this PR and then add new material in another PR.

Sure. I will add tight_cut_decomposition() in a different PR. In fact, that methods need some more work.

For now, with that method in hold, I have half implemented bricks_and_braces() (a small method), where actually one of the outputs (that is nontrivial_odd_component) of the above two methods (in this PR) are getting used. While doing so, I just saw that instead of returning a single nontrivial_odd_component, if we return all possible relevant nontrivial_odd_components in the above two methods, in other methods, the running time can be improved (even though the complexity remains the same theoretically).

janmenjayap · 2024-12-27T15:46:09Z

src/sage/graphs/matching_covered_graph.py

+            H.delete_vertices([u, v])
+
+            if not H.is_matching_covered(list(matching - set([e]))):
+                if not coNP_certificate:


I was just playing with some more examples and it turned out that I have not implemented the exception handling properly, yet.

For instance, if we take the original graph to be a Ladder Graph on 6 or more vertices, this check of whether that graph is matching covered raises an error instead of returning False, as H is not connected anymore. This one is to be checked and implemented.

janmenjayap added 4 commits December 1, 2024 13:25

added is_brace()

66e9724

updated the to do list

86bd2e9

updated the digraph H

dc47497

updated the doctest

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github-actions bot added the s: needs review label Dec 1, 2024

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janmenjayap and others added 5 commits December 1, 2024 17:08

updated is_matching_covered()

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updated is_brace()

0eb894d

Merge branch 'develop' into bricks_and_braces

ce1e3aa

removed an unnecessary space

451f164

updated the documentation

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updated is_brace()

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user202729 reviewed Dec 3, 2024

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janmenjayap and others added 2 commits December 5, 2024 22:17

Updated math expression formatting

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Co-authored-by: user202729 <[email protected]>

Merge branch 'develop' into bricks_and_braces

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janmenjayap and others added 3 commits December 13, 2024 08:52

Merge branch 'develop' into bricks_and_braces

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added is_brick()

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updated is_brace()

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janmenjayap and others added 3 commits December 16, 2024 18:41

Merge branch 'develop' into bricks_and_braces

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updated is_brick()

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updated is_brace()

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janmenjayap and others added 13 commits December 21, 2024 11:29

updated see also

e101d33

Merge branch 'bricks_and_braces' of https://github.com/janmenjayap/sage…

b2f917d

… into bricks_and_braces

updated the doctests

b7c274e

updated connected components parameter

b8fdab8

updated the return statement of is_brick()

cb4d3d1

updated the return statement of is_brace()

d670168

updated is_brace()

03771ee

updated is_brick()

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updated doctests

d295290

updated the doctests

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Merge branch 'develop' into bricks_and_braces

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introduced tight_cut_decomposition()

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removed a whitespace

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janmenjayap commented Dec 27, 2024

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janmenjayap and others added 6 commits January 1, 2025 20:09

updated is_brace()

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updated is_brick()

e4ceffe

added tight_cut_decomposition() to todo list

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added a missing whitespace

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fixed RST215 error

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Implemented methods concerning bricks and braces of a matching covered graph #39065

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