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Overwrote methods concerning connectivity in a matching covered graph #39657

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janmenjayap
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The objective of this PR is to overwrite the methods pertaining to connectivity in a matching covered graph.

More specifically, this PR aims to overwrite the following methods:

  • is_biconnected() | Check whether the (matching covered) graph is biconnected.
  • is_connected() | Check whether the (matching covered) graph is connected.

📌 Todo

  • Add the list of other relevant methods to overwrite (so that the computation time is asymptotically shorter).

Fixes #38216.
Please 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

Nothing as of now.

cc: @dcoudert.

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github-actions bot commented Mar 9, 2025

Documentation preview for this PR (built with commit d118383; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

@dcoudert
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dcoudert commented Mar 9, 2025

If this PR is only for is_biconnected, which is certainly enough, you could change the title of the PR to better reflect the content, like "add method is_biconnected to matching covered graph".

@janmenjayap
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HI,
There are some other small (and kind of more or less not so complicated) methods related to connectivity, that are to be overwritten, for instance is_connected(), is_path(), is_tree() etc. We may incorporate all of those small and simple methods in this PR.

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On Decompositions, Generation Methods and related concepts in the theory of Matching Covered Graphs
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