def _testMatching():
g = SimpleGraph()
verts = list(range(7))
g.addVertices(verts)
assert g.isMatching()
g.addEdge(0, 1)
assert g.isMatching()
g.addEdge(1, 2)
assert not g.isMatching()
g.addEdge(2, 3)
g.addEdge(4, 5)
assert not g.isMatching()
g.removeEdge(1, 2)
assert g.isMatching()
assert not g.isPerfectMatching()
g.addEdge(6, g.pushVertex())
assert g.isPerfectMatching()
g = _build4by4()
assert not g.isMatching()
assert g.maximumMatching().isPerfectMatching()
v_a = g.pushVertex()
g.addEdge(0, v_a)
m = g.maximumMatching()
assert m.isMatching()
assert not m.isPerfectMatching()
v_b = g.pushVertex()
g.addEdge(v_a, v_b)
assert g.maximumMatching().isPerfectMatching()
g.addEdge(v_b, 4)
assert g.maximumMatching().isPerfectMatching()
g = SimpleGraph()
A = _makeChain(g, 9)
assert not g.isCycle(A)
assert g.maximumMatching().edgeCount() == 4
g.addEdge(A[0], A[-1])
assert g.isCycle(A)
assert g.maximumMatching().edgeCount() == 4
hub = g.pushVertex()
for Av in A:
g.addEdge(hub, Av)
assert g.maximumMatching().isPerfectMatching()
for Av in A:
g.addEdge(Av, _makeLoop(g, 5)[0])
assert not g.maximumMatching().isPerfectMatching()
g.removeVertex(hub)
assert g.maximumMatching().isPerfectMatching()
g = _build4by4()
g.removeVertices([4, 8, 3, 15])
assert g.maximumMatching().isPerfectMatching()
def _build4by4():
# makes a grid structure like:
# 0 - 1 - 2 - 3
# ! ! ! !
# 4 - 5 - 6 - 7
# ! ! ! !
# 8 - 9 - 10- 11
# ! ! ! !
# 12- 13- 14- 15
g = SimpleGraph()
g.addVertices(range(16))
for k in range(0, 16, 4):
for i in range(k, k + 3):
g.addEdge(i, i + 1)
for k in range(4):
for i in range(k, 12, 4):
g.addEdge(i, i + 4)
for i in [0, 3, 12, 15]:
assert g.degree(i) == 2
for i in [1, 2, 7, 11, 14, 13, 8, 4]:
assert g.degree(i) == 3
for i in [5, 6, 9, 10]:
assert g.degree(i) == 4
return g