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updated is_brick()
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src/sage/graphs/matching_covered_graph.py

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@@ -2751,7 +2751,7 @@ def is_brick(self, coNP_certificate=False):
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- If the input nonbipartite matching covered graph is a brick, a
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boolean ``True`` is returned if ``coNP_certificate`` is set to
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``False`` otherwise a 4-tuple ``(True, None, None, None)`` is
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``False``, otherwise a 4-tuple ``(True, None, None, None)`` is
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returned.
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- If the input nonbipartite matching covered graph is not a brick, a
@@ -2763,20 +2763,20 @@ def is_brick(self, coNP_certificate=False):
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1. a boolean ``False``,
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2. a list of list of edges each list constituting a nontrivial tight
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cut collectively representing a laminar tight cut,
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2. a list of lists of edges, each list constituting a nontrivial
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tight cut collectively representing a laminar tight cut,
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3. a list of set of vertices of one of the shores of those respective
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nontrivial tight cuts.
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nontrivial tight cuts:
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- In case of nontrivial barrier cuts, each of the shores is a
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nontrivial odd component wrt a nontrivial barrier, thus the
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returned list forms mutually exclusive collection of (odd)
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sets.
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#. In case of nontrivial barrier cuts, each of the shores is a
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nontrivial odd component with respect to a nontrivial barrier,
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thus the returned list forms mutually exclusive collection of
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(odd) sets.
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- Otherwise each of the nontrivial tight cuts is a 2-separation
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cut, each of the shores form a subset sequence, with the `i`th
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shore being a proper subset of the `i + 1`th shore.
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#. Otherwise each of the nontrivial tight cuts is a 2-separation
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cut, each of the shores form a subset sequence, with the
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`i` th shore being a proper subset of the `i + 1` th shore.
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4. a string showing whether the nontrivial tight cuts are barrier
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cuts (if the string is 'nontrivial barrier cuts'), or 2-separation

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