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sagemathgh-38218: Implementing `is_matching_covered()` and `is_bicritical()`
    
<!-- ^ Please provide a concise and informative title. -->
The objective of this issue is to implement  `is_matching_covered()` and
`is_bicritical()` and to collect the matching related methods and to put
them under `matching.py`.
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
This PR introduces two methods pertaining to matching and aims to list
out all matching related functions in `matching.py`. The two new methods
are described below:

- [x] `is_matching_covered()`: Check if the graph is matching covered.
- [x] `is_bicritical()`: Check if the graph is bicritical.

<!-- v Why is this change required? What problem does it solve? -->
This PR addresses couple of missing functions and also addresses the
lack of a separate file for matchings.
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->
Fixes sagemath#38216.



### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

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

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
Nothing as of now (up to my knowledge).
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->

cc: @dcoudert.
    
URL: sagemath#38218
Reported by: Janmenjaya Panda
Reviewer(s): David Coudert, Janmenjaya Panda
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1 change: 1 addition & 0 deletions src/doc/en/reference/graphs/index.rst
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Expand Up @@ -84,6 +84,7 @@ Libraries of algorithms
sage/graphs/spanning_tree
sage/graphs/pq_trees
sage/graphs/trees
sage/graphs/matching
sage/graphs/matchpoly
sage/graphs/genus
sage/graphs/lovasz_theta
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10 changes: 10 additions & 0 deletions src/doc/en/reference/references/index.rst
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Expand Up @@ -4666,6 +4666,12 @@ REFERENCES:
measures*. Publications Mathématiques de l'Institut des
Hautes Études Scientifiques 98(1) (2003), pp. 167-212.
.. [LZ2001] Dingjun Lou and Ning Zhong. *A highly efficient algorithm to
determine bicritical graphs.* In: Wang, J. (eds) Computing and
Combinatorics. Lecture Notes in Computer Science, vol 2108,
pages 349--356. Springer, Berlin, Heidelberg, 2001,
:doi:`10.1007/3-540-44679-6_38`.
.. [LZ2004] S. Lando and A. Zvonkine, "Graphs on surfaces and their
applications", Springer-Verlag, 2004.
Expand Down Expand Up @@ -6510,6 +6516,10 @@ REFERENCES:
.. [TTWL2009] Trebst, Troyer, Wang and Ludwig, A short introduction to
Fibonacci anyon models, :arxiv:`0902.3275`.
.. [Tut1947] W.T. Tutte. *The factorization of linear graphs.* Journal of the
London Mathematical Society, vol. s1-22, issue 2, pages 107--111,
April 1947. :doi:`10.1112/jlms/s1-22.2.107`.
.. [Tur1974] \R. J. Turyn *Hadamard matrices, Baumert-Hall units,
four-symbol sequences, pulse compression, and surface wave encodings*.
Journal of Combinatorial Theory, Series A 16.3 (1974), pp 313–333.
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