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cleaned up the code
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@janmenjayap
janmenjayap committed Jun 23, 2024
1 parent 91a0460 commit 20aa1f1
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65 changes: 31 additions & 34 deletions src/sage/graphs/graph.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -4388,8 +4388,8 @@ def M_alternating_even_mark(self, vertex, matching):
sage: M = Graph(G.matching())
sage: G.is_factor_critical(M)
True
sage: for v in G.vertices():
....: if v not in M.vertices():
sage: for v in G:
....: if v not in M:
....: break
....:
sage: S = G.M_alternating_even_mark(v, M)
Expand Down Expand Up @@ -4427,7 +4427,8 @@ def M_alternating_even_mark(self, vertex, matching):
sage: M = Graph(G.matching())
sage: G.is_bicritical(M)
True
sage: u = random.choice(G.vertices()) # needs random
sage: import random
sage: u = random.choice(G.vertices()) # needs random
sage: v = next(M.neighbor_iterator(u))
sage: S = G.M_alternating_even_mark(u, M)
sage: S == (set(G.vertices()) - {v})
Expand Down Expand Up @@ -4471,11 +4472,10 @@ def M_alternating_even_mark(self, vertex, matching):
:meth:`~sage.graphs.graph.Graph.is_matching_covered`,
:meth:`~sage.graphs.graph.Graph.is_bicritical`
"""

G = self.to_simple()

# The input vertex must be a valid vertex of the graph
if vertex not in G.vertices():
if vertex not in self:
raise ValueError("'{}' is not a vertex of the graph".format(vertex))

# The input matching must be a valid matching of the graph
Expand All @@ -4497,8 +4497,8 @@ def M_alternating_even_mark(self, vertex, matching):
predecessor = {vertex: vertex}
rank = {vertex: 0}

if vertex in M.vertices():
u = M.neighbors(vertex)[0]
if vertex in M:
u = next(M.neighbor_iterator(vertex))
predecessor[u] = None
rank[u] = -1
odd.add(u)
Expand All @@ -4513,6 +4513,7 @@ def M_alternating_even_mark(self, vertex, matching):
ancestor_x = [x]
ancestor_y = [y]

# Loop over until the nearest common ancestor of x and y is reached
while ancestor_x[-1] != ancestor_y[-1]:
if rank[ancestor_x[-1]] > rank[ancestor_y[-1]]:
ancestor_x.append(predecessor[ancestor_x[-1]])
Expand All @@ -4526,16 +4527,17 @@ def M_alternating_even_mark(self, vertex, matching):
ancestor_y.pop()
# Set t as pred of all vertices of the chains and add
# vertices marked odd to the queue
next_rank_to_lcs_rank = rank[lcs] + 1
for a in itertools.chain(ancestor_x, ancestor_y):
predecessor[a] = lcs
rank[a] = rank[lcs] + 1
rank[a] = next_rank_to_lcs_rank

if a in odd:
even.add(a)
odd.discard(a)
q.put(a)

elif y in M.vertices():
elif y in M:
# y has not been visited yet
z = next(M.neighbor_iterator(y))
odd.add(y)
Expand Down Expand Up @@ -4785,7 +4787,7 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
If set to ``None``, a matching is computed using the other parameters.
- ``algorithm`` -- string (default: ``Edmonds``); the algorithm to be
- ``algorithm`` -- string (default: ``'Edmonds'``); the algorithm to be
used to compute a maximum matching of the graph among
- ``'Edmonds'`` selects Edmonds' algorithm as implemented in NetworkX,
Expand Down Expand Up @@ -4859,19 +4861,19 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
sage: H.is_bicritical()
True
A graph with more that one component is not bicritical::
A graph (of order more than two) with more that one component is not bicritical::
sage: cycle1 = graphs.CycleGraph(4)
sage: cycle2 = graphs.CycleGraph(6)
sage: cycle2.relabel(lambda v: v + 4)
sage: G = Graph()
sage: G.add_edges(cycle1.edges() + cycle2.edges())
sage: len(G.connected_components())
sage: len(G.connected_components(sort=False))
2
sage: G.is_bicritical()
False
Graphs (of order more than two) with cut-vertices are not bicritical::
A graph (of order more than two) with a cut-vertex is not bicritical::
sage: G = graphs.CycleGraph(6)
sage: G.add_edges([(5, 6), (5, 7), (6, 7)])
Expand All @@ -4891,7 +4893,7 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
sage: G.is_bicritical()
True
Bipartite graphs of order three or more are not bicritical::
A bipartite graph of order three or more is not bicritical::
sage: G = graphs.CompleteBipartiteGraph(3, 3)
sage: G.has_perfect_matching()
Expand All @@ -4903,11 +4905,11 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
sage: G = graphs.WheelGraph(10)
sage: M = G.matching()
sage: G.is_bicritical(M)
sage: G.is_bicritical(matching=M)
True
sage: H = graphs.HexahedralGraph()
sage: N = H.matching()
sage: H.is_bicritical()
sage: H.is_bicritical(matching=N)
False
One may ask for a co-`\mathcal{NP}` certificate::
Expand Down Expand Up @@ -4959,10 +4961,10 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
REFERENCES:
- [LZ2001]_
- [LM2024]_
- [LZ2001]_
.. SEEALSO::
:meth:`~sage.graphs.graph.Graph.is_factor_critical`,
:meth:`~sage.graphs.graph.Graph.is_matching_covered`,
Expand All @@ -4973,7 +4975,6 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
- Janmenjaya Panda (2024-06-17)
"""

# The graph must be nontrivial
if self.order() < 2:
raise ValueError("the graph is trivial")
Expand All @@ -4991,7 +4992,7 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
if not coNP_certificate:
return False

components = self.connected_components()
components = self.connected_components(sort=False)

# Check if there is an odd component with at least three vertices
for component in components:
Expand All @@ -5018,15 +5019,11 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal
if not coNP_certificate:
return False

from sage.graphs.bipartite_graph import BipartiteGraph
H = BipartiteGraph(self)
color_class_A, color_class_B = H.bipartition()
del H
A, B = self.bipartite_sets()

if len(color_class_A) > 1:
return (False, set(list(color_class_A)[:2]))
else:
return (False, set(list(color_class_B)[:2]))
if len(A) > 1:
return (False, set(list(A)[:2]))
return (False, set(list(B)[:2]))

if matching:
# The input matching must be a valid perfect matching of the graph
Expand All @@ -5044,29 +5041,29 @@ def is_bicritical(self, matching=None, algorithm='Edmonds', coNP_certificate=Fal

# It must be a perfect matching
if self.order() != M.order():
return (False, set([M.edges[0][0], M.edges[0][1]])) if coNP_certificate else False
return (False, set([M.edges()[0][0], M.edges()[0][1]])) if coNP_certificate else False

# G is bicritical iff for each vertex u with its M-matched neighbor being v,
# G is bicritical if and only if for each vertex u with its M-matched neighbor being v,
# every vertex of the graph distinct from v must be reachable from u through an even length
# M-alternating uv-path starting with an edge not in M and ending with an edge in M

for u in self.vertices():
for u in self:
v = next(M.neighbor_iterator(u))

even = self.M_alternating_even_mark(u, M)

for w in self.vertices():
for w in self:
if w != v and w not in even:
return (False, set([v, w])) if coNP_certificate else False

return (True, None) if coNP_certificate else True

@doc_index("Leftovers")
def is_matching_covered(self):
def is_matching_covered(self, *_, **__):
r"""
Check if the graph is matching covered.
"""
pass
raise NotImplementedError()

@doc_index("Algorithmically hard stuff")
def has_homomorphism_to(self, H, core=False, solver=None, verbose=0,
Expand Down
104 changes: 52 additions & 52 deletions src/sage/graphs/matching_covered_graph.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -21,80 +21,80 @@


class MatchingCoveredGraph(Graph):
def __init__(self):
pass
def __init__(self, *_, **__):
raise NotImplementedError()

def _upgrade_from_graph(self):
pass
def _upgrade_from_graph(self, *_, **__):
raise NotImplementedError()

def __repr__(self):
pass
def __repr__(self, *_, **__):
raise NotImplementedError()

def plot(self):
pass
def plot(self, *_, **__):
raise NotImplementedError()

def maximal_barrier(self):
pass
def maximal_barrier(self, *_, **__):
raise NotImplementedError()

def canonical_partition(self):
pass
def canonical_partition(self, *_, **__):
raise NotImplementedError()

def tight_cut_decomposition(self):
pass
def tight_cut_decomposition(self, *_, **__):
raise NotImplementedError()

def bricks_and_braces(self):
pass
def bricks_and_braces(self, *_, **__):
raise NotImplementedError()

def number_of_bricks(self):
pass
def number_of_bricks(self, *_, **__):
raise NotImplementedError()

def number_of_braces(self):
pass
def number_of_braces(self, *_, **__):
raise NotImplementedError()

def number_of_petersen_bricks(self):
pass
def number_of_petersen_bricks(self, *_, **__):
raise NotImplementedError()

def is_brick(self):
pass
def is_brick(self, *_, **__):
raise NotImplementedError()

def is_brace(self):
pass
def is_brace(self, *_, **__):
raise NotImplementedError()

def is_removable_edge(self):
pass
def is_removable_edge(self, *_, **__):
raise NotImplementedError()

def removable_edges(self):
pass
def removable_edges(self, *_, **__):
raise NotImplementedError()

def is_removable_doubleton(self):
pass
def is_removable_doubleton(self, *_, **__):
raise NotImplementedError()

def removable_doubletons(self):
pass
def removable_doubletons(self, *_, **__):
raise NotImplementedError()

def retract(self):
pass
def retract(self, *_, **__):
raise NotImplementedError()

def ear_decomposition(self):
pass
def ear_decomposition(self, *_, **__):
raise NotImplementedError()

def is_b_invariant_edge(self):
pass
def is_b_invariant_edge(self, *_, **__):
raise NotImplementedError()

def is_thin_edge(self):
pass
def is_thin_edge(self, *_, **__):
raise NotImplementedError()

def is_strictly_thin_edge(self):
pass
def is_strictly_thin_edge(self, *_, **__):
raise NotImplementedError()

def is_mccuaig_brace(self):
pass
def is_mccuaig_brace(self, *_, **__):
raise NotImplementedError()

def brace_generation_sequence(self):
pass
def brace_generation_sequence(self, *_, **__):
raise NotImplementedError()

def is_norine_thomas_brick(self):
pass
def is_norine_thomas_brick(self, *_, **__):
raise NotImplementedError()

def brick_generation_sequence(self):
pass
def brick_generation_sequence(self, *_, **__):
raise NotImplementedError()

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