Overwrote methods concerning connectivity in a matching covered graph

src/sage/graphs/matching_covered_graph.py

@@ -57,7 +57,6 @@
         ``delete_multiedge()`` | Delete all edges from ``u`` to ``v``.
         ``disjoint_union()`` | Return the disjoint union of ``self`` and ``other``.
         ``disjunctive_product()`` | Return the disjunctive product of ``self`` and ``other``.
-        ``is_biconnected()`` | Check if the matching covered graph is biconnected.
         ``is_block_graph()`` | Check whether the matching covered graph is a block graph.
         ``is_cograph()`` | Check whether the matching covered graph is cograph.
         ``is_forest()`` | Check if the matching covered graph is a forest, i.e. a disjoint union of trees.
@@ -2345,6 +2344,56 @@ def has_perfect_matching(G, algorithm='Edmonds', solver=None, verbose=0,
         raise ValueError('algorithm must be set to \'Edmonds\', '
                          '\'LP_matching\' or \'LP\'')
 
+    @doc_index('Overwritten methods')
+    def is_biconnected(self):
+        r"""
+        Check whether the (matching covered) graph is biconnected.
+
+        A biconnected graph is a connected graph on two or more vertices that
+        is not broken into disconnected pieces by deleting any single vertex.
+        By definition of matching covered graphs, it follows that a graph, that
+        is matching covered, is biconnected.
+
+        Observe that `K_2` (upto multiple edges) is biconnected. A matching
+        covered graph `G`, that is not `K_2` (upto multiple edges), has at
+        least four vertices and four edges. Consider any two adjacent edges
+        (`e` and `f`) of `G`. Take a perfect matching `M` of `G` containing
+        the edge `e` and a different perfect matching `N` of `G` containing
+        the edge `f`. Observe that the symmetric difference of `M` and `N`
+        has a cycle containing both of the edges `e` and `f`. Thus, each edge
+        of `G` is contained in some cycle of `G`. Therefore, `G` is
+        biconnected.
+
+        .. NOTE::
+
+            This method overwrites the
+            :meth:`~sage.graphs.graph.Graph.is_biconnected` method
+            in order to return ``True`` as matching covered graphs are
+            biconnected.
+
+        EXAMPLES:
+
+        The complete graph on two vertices is the smallest biconnected graph
+        that is matching covered::
+
+            sage: K2 = graphs.CompleteGraph(2)
+            sage: G = MatchingCoveredGraph(K2)
+            sage: G.is_biconnected()
+            True
+
+        Petersen graph is matching covered and biconnected::
+
+            sage: P = graphs.PetersenGraph()
+            sage: G = MatchingCoveredGraph(P)
+            sage: G.is_biconnected()
+            True
+
+        .. SEEALSO::
+
+            - :meth:`~sage.graphs.matching_covered_graph.MatchingCoveredGraph.is_connected`
+        """
+        return True
+
     @doc_index('Bricks, braces and tight cut decomposition')
     def is_brace(self, coNP_certificate=False):
         r"""