def testEvenHoleFree(self):
g = make_cycle(4)
self.assertEqual(even_hole_free(g), False)
g = make_cycle(5)
self.assertEqual(even_hole_free(g), True)
g = make_cycle(10)
self.assertEqual(even_hole_free(g), False)
def testColoringHardGraph(self):
# C5 + 5 Xi
g = make_cycle(5)
index = 0
for i in range(5, 10):
g.add_node(i)
# make it a two vertex
g.add_edge(i, (index+0) % 5) # xi
g.add_edge(i, (index+1) % 5)
index += 1
g.add_edge(5, 6)
g.add_edge(5, 8)
g.add_edge(6, 8)
g.add_edge(7, 9)
self.dcolor = Dcolor(g)
color = self.dcolor.color()
expect = [[1, 8, 9], [5, 4, 7], [2], [0, 3, 6]]
self.assertEqual(self.dcolor.valid_coloring(color), True)
self.assertEqual(color, expect)
# C5 + 2 Yi
g = make_cycle(5)
g.add_node(5)
g.add_edge(0,5)
g.add_edge(1,5)
g.add_edge(2,5)
g.add_node(6)
g.add_edge(0,6)
g.add_edge(3,6)
g.add_edge(4,6)
self.dcolor = Dcolor(g)
color = self.dcolor.color()
expect = [[0, 3], [1, 4], [5, 6], [2]]
self.assertEqual(self.dcolor.valid_coloring(color), True)
self.assertEqual(color, expect)
def go():
forbidden = [make_clique(4), make_cycle(4), make_clique(6), make_cycle(8)]
onlyfiles = [ f for f in listdir(MYPATH) if isfile(join(MYPATH,f)) ]
for f in onlyfiles:
print("Working on:")
print(f)
g = File(MYPATH,file=f).load(f)
check_graph(DROPS, g, forbidden)
return
def go():
forbidden = [make_co_cricket(),
make_cycle(4),
make_cycle(6),
make_cycle(8),
make_wheel(6)]
g = make_cycle(7)
check_graph(DROPS, g, forbidden)
return
def go():
forbidden = [make_kite(),
make_cycle(4),
make_cycle(6),
make_cycle(8),
make_wheel(6)]
g = make_cycle(5)
check_graph(DROPS, g, forbidden)
return
def testOddHoleFree(self):
g = make_cycle(4)
self.assertEqual(odd_hole_free(g), True)
g = make_cycle(5)
self.assertEqual(odd_hole_free(g), False)
g = make_cycle(10)
self.assertEqual(odd_hole_free(g), True)
g = make_cycle(11)
self.assertEqual(odd_hole_free(g), False)
def testEvenHoleFree(self):
g = make_cycle(4)
self.assertEqual(even_hole_free(g).edges(), g.edges())
self.assertEqual(even_hole_free(g).nodes(), g.nodes())
g = make_cycle(5)
self.assertEqual(even_hole_free(g), None)
g = make_cycle(10)
self.assertEqual(even_hole_free(g).edges(), g.edges())
self.assertEqual(even_hole_free(g).nodes(), g.nodes())
def TheAlgorithm(G):
dColor = Dcolor(G)
partialColoring = list()
#Compute chi(G) (using brute force)
k = len(dColor.color())
hasStrongStableSet = False
thisStableSet = FindStrongStableSet(G)
if thisStableSet != None:
hasStrongStableSet = True
while hasStrongStableSet:
#thisStableSet = FindStrongStableSet(G)
partialColoring.append(list(thisStableSet))
#Remove this stable set from the graph
for thisStableVertex in thisStableSet:
G.remove_node(thisStableVertex)
thisStableSet = FindStrongStableSet(G)
if thisStableSet == None:
hasStrongStableSet = False
#check for induced C7
graphToTest = convert_node_labels_to_integers(G, 0, ordering='default', label_attribute = None)
if induced_subgraph(graphToTest, make_cycle(CYCLE_LENGTH)) == None:
stillHasInducedC7 = False
else:
stillHasInducedC7 = True
graphToTest.clear()
while stillHasInducedC7 == True:
thisStableSet = FindSimpleStableSet(G)
partialColoring.append(thisStableSet)
for thisStableVertex in thisStableSet:
G.remove_node(thisStableVertex)
graphToTest = convert_node_labels_to_integers(G, 0, ordering='default', label_attribute = None)
if induced_subgraph(graphToTest, make_cycle(CYCLE_LENGTH)) == None:
stillHasInducedC7 = False
graphToTest.clear()
"""
At this point, there does not exist a strong stable set of size 3, because there is no C7.
This means that G is now a perfect graph.
"""
t = chromatic_number(G)
#Find the chromatic number of our partial graph of stable sets
s = len(partialColoring)
if k == (s + t):
result = True
else:
result = False
return result
def testOddHoleFree(self):
g = make_cycle(4)
self.assertEqual(odd_hole_free(g), None)
g = make_cycle(5)
self.assertEqual(odd_hole_free(g).edges(), g.edges())
self.assertEqual(odd_hole_free(g).nodes(), g.nodes())
g = make_cycle(10)
self.assertEqual(odd_hole_free(g), None)
g = make_cycle(11)
self.assertEqual(odd_hole_free(g).edges(), g.edges())
self.assertEqual(odd_hole_free(g).nodes(), g.nodes())
def testForbidden(self):
claw = make_claw()
c4 = make_cycle(4)
cok4 = make_cok4()
g = make_cycle(5)
not_allowed = [claw, c4, cok4]
gen = Generator2(g, 1, forbidden=not_allowed)
for graph in gen.iterate():
for h in not_allowed:
if induced_subgraph(graph, h) is not None:
print(graph.edges())
print(h.edges())
self.assertEqual(True, False ,"Failed to forbid a graph")
def testColoringCritical(self):
self.dcolor = Dcolor(make_cycle(5))
color = self.dcolor.color()
expect = [[0], [1, 3], [2, 4]]
self.assertEqual(len(color), 3)
self.assertEqual(color, expect)
k1 = nx.Graph()
k1.add_node(0)
g = join(make_cycle(5), k1)
self.dcolor = Dcolor(g)
color = self.dcolor.color()
self.assertEqual(len(color), 4)
expect = [[5], [0], [1, 3], [2, 4]]
self.assertEqual(expect, color)
def testColoringClique(self):
g = make_cycle(3)
self.dcolor = Dcolor(g)
color = self.dcolor.color()
expect = [[0], [1], [2]]
self.assertEqual(len(color), 3)
self.assertEqual(color, expect)
def Process():
for thisXConfiguration in product(range(MAX_X_CARDINALITY), repeat = BASE_CYCLE_SIZE):
baseGraph = make_cycle(7)
baseGraph, x_sets = ConstructGraph(thisXConfiguration, baseGraph)
thisGraph = deepcopy(baseGraph)
print(thisGraph.edges())
#Try all possible combos of X and X_i+2 edges
for xSetIndex in range(0,BASE_CYCLE_SIZE):
s1 = x_sets[xSetIndex]
s2 = x_sets[(xSetIndex + 2) % BASE_CYCLE_SIZE]
for i in range(0,4):
for thisEdgeCombo in combinations(product(s1,s2),i):
for thisEdge in thisEdgeCombo:
thisGraph.add_edge(thisEdge[0], thisEdge[1])
WriteToLogFile(FinalProcessGraph(thisGraph))
#for each of these combos, try it with all combos of X and X_i+5
thisGraphMoreJoins = deepcopy(thisGraph)
s1 = x_sets[xSetIndex]
s2 = x_sets[(xSetIndex + 5) % BASE_CYCLE_SIZE]
for i in range(0,4):
for thisEdgeCombo in combinations(product(s1,s2),i):
for thisEdge in thisEdgeCombo:
thisGraphMoreJoins.add_edge(thisEdge[0], thisEdge[1])
WriteToLogFile(FinalProcessGraph(thisGraphMoreJoins))
thisGraph = deepcopy(baseGraph)
baseGraph.clear()
return
def testC5DiamondCoDiamondFree(self):
g = make_cycle(5)
subgraphs = [make_diamond(), make_co_diamond()]
k_vertexes = k_vertex(g, subgraphs)
expect = [False, False, True, True, False, False]
for index, k in enumerate(k_vertexes):
self.assertEqual(k['has_k_vertex'], expect[index],
'''K Vertex says (diamond,co-diamond)- free Graph
%d - vertex:%r but should be %r'''
%(index, k['has_k_vertex'], expect[index]))
set_2_vertex = [(0, 1), (0, 4), (1, 2), (2, 3), (3, 4)]
for check in set_2_vertex:
self.assertEqual(check in k_vertexes[2]['combinations'], True,
'''
K vertex missing 2 Vertex set (%d, %d)
on (diamond, co-diamond)-free Grpah
''' %(check[0],check[1]))
set_3_vertex = [(0, 1, 3),
(0, 2, 3),
(0, 2, 4),
(1, 2, 4),
(1, 3, 4)]
for check in set_3_vertex:
self.assertEqual(check in k_vertexes[3]['combinations'], True,
'''
K vertex missing 3 Vertex set (%d, %d, %d)
on (diamond, co-diamond)-free Grpah
''' %(check[0],check[1], check[2]))
def process():
index = 0
#Generate an array corresponding to the k-vertices we want to add to c7
for add in combinations_with_replacement(range(4), 7):
print(add)
#We can have at most 3 Z's and 2 Y's, making 5 possible vertices we can add
if count(add) > 5:
break
for thisPermutation in permutations(add):
#copy initial graph (c7) and add vertices
#self.g = BASE.copy()
g = make_cycle(7)
add_vertices(g, thisPermutation)
check = True
#we want our graph to remain {4k1,c4,c6}-free
for H in FORBIDDEN:
if induced_subgraph(g, H):
check = False
break
if check:
#log it
f = File(DIRECTORY, G=g, logger=LOGGER, base="C5-")
fp = f.save()
if fp is not None:
index += 1
print("Created Graph: %d" % index)
def Construct():
resultGraph = make_cycle(CYCLE_LENGTH)
x_sets = [ [] for i in range(0,CYCLE_LENGTH)]
#Add the nodes
for vertexIndex in range(0, NUMBER_OF_LAYERS * CYCLE_LENGTH):
#add the new node
vertexToAddNum = resultGraph.number_of_nodes()
resultGraph.add_node(vertexToAddNum)
x_sets[vertexIndex % CYCLE_LENGTH].append(vertexToAddNum)
#add its edges
resultGraph.add_edge( (vertexToAddNum - 1) % CYCLE_LENGTH, vertexToAddNum )
resultGraph.add_edge( vertexToAddNum % CYCLE_LENGTH, vertexToAddNum)
resultGraph.add_edge( (vertexToAddNum + 1) % CYCLE_LENGTH, vertexToAddNum)
#x_i forms a clique
for thisXSet in x_sets:
if(len(thisXSet) > 1):
for thisCliqueEdge in product(thisXSet, thisXSet):
if(thisCliqueEdge[0] != thisCliqueEdge[1]):
resultGraph.add_edge(thisCliqueEdge[0], thisCliqueEdge[1])
#X_i joins its neighbours
for thisXSetIndex in range(0,CYCLE_LENGTH):
x1 = x_sets[thisXSetIndex]
x2 = x_sets[(thisXSetIndex+1) % CYCLE_LENGTH]
for vertexI in x1:
for vertexJ in x2:
resultGraph.add_edge(vertexI,vertexJ)
return resultGraph
def TestAdjacentToVertices(self):
expect = adjacent_to_vertices(-1, [0, 1], make_claw())
self.assertEqual(expect, False)
expect = adjacent_to_vertices(0, [1, 2, 3], make_claw())
self.assertEqual(expect, True)
expect = adjacent_to_vertices(0, [2, 3], make_cycle(5))
self.assertEqual(expect, False)
def ConstructBaseGraph():
global CURRENT_X_SETS, CURRENT_Y_SETS
CURRENT_X_SETS = [ [i] for i in range(0, CYCLE_LENGTH)]
CURRENT_Y_SETS = [ [] for i in range(0, CYCLE_LENGTH)]
result = make_cycle(CYCLE_LENGTH)
return deepcopy(result)
def testColorCycle(self):
g = make_cycle(5)
for i in range(5, 100):
g.add_node(i)
g.add_edge(i - 1, i)
self.dcolor = Dcolor(g)
color = self.dcolor.color()
self.assertEqual(len(color), 3)
self.assertEqual(self.dcolor.valid_coloring(color), True)
def testTriangleFree(self):
G = make_cycle(4)
self.assertEqual(triangle_free(G), True)
G = make_claw()
self.assertEqual(triangle_free(G), True)
G = make_co_claw()
self.assertEqual(triangle_free(G), False)
G = make_diamond()
self.assertEqual(triangle_free(G), False)
def testTotalGraphs(self):
G = nx.Graph()
G.add_node(0)
self.gen = Generator(G, 2, [])
result = self.gen.total_graphs()
self.assertEqual(10, result)
G = make_cycle(5)
self.gen = Generator(G, 5, [])
result = self.gen.total_graphs()
self.assertEqual(34427111456, result)
def even_hole_free(G):
i_set = graph_clique_number(complement(G))
free = True
i = 4
while i <= i_set * 2 and free:
g = make_cycle(i)
if induced_subgraph(G, g):
free = False
i += 2
return free
def testLoad(self):
claw = make_claw()
c7 = make_cycle(7)
co_claw = make_co_claw()
tests = {"test1.txt": claw, "test2.txt": c7, "test3.txt": co_claw}
directory = os.path.join(self.directory, "test")
for file, expect in tests.items():
file_obj = File(directory, file=file)
self.assertEqual(expect.nodes(), file_obj.G.nodes(), "Load Failed Nodes: %s" % file)
self.assertEqual(expect.edges(), file_obj.G.edges(), "Load Failed :Edges %s" % file)
def testCheckCondition(self):
test = check_condition_holds(make_clique(5))
expect = False
self.assertEqual(test, expect)
test = check_condition_holds(make_clique(3))
expect = False
self.assertEqual(test, expect)
test = check_condition_holds(make_cycle(5))
expect = True
self.assertEqual(test, expect)
def critical_cycle(n):
g = make_cycle(n)
v1 = n
v2 = n+1
g.add_node(v1)
g.add_node(v2)
for i in range(0, n // 2 + 1):
g.add_edge(i, v1)
g.add_edge(n-i-1, v2)
return g
def even_hole_free(G):
i_set = graph_clique_number(complement(G))
free = None
i = 4
while i <= i_set * 2 and free is None:
g = make_cycle(i)
induced = induced_subgraph(G, g)
if induced is not None:
free = induced
i += 2
return free
def testColoringCritical(self):
c5 = make_cycle(5)
color = coloring(c5)
expect = [[4, 1], [3, 0], [2]]
self.assertEqual(len(color), 3)
self.assertEqual(color, expect)
k1 = nx.Graph()
k1.add_node(0)
g = join(c5, k1)
color = coloring(g)
self.assertEqual(len(color), 4)
expect = [[4], [3, 1], [2, 0], [5]]
self.assertEqual(expect, color)
def testGetName(self):
g = make_claw()
f = File(self.directory, G=g, logger=self.logger)
self.assertEqual(f.get_name(), "has_K2_edges-3_nodes-4.txt")
g = make_cycle(5)
f = File(self.directory, G=g, logger=self.logger)
self.assertEqual(f.get_name(), "has_K2_edges-5_nodes-5.txt")
self.assertEqual(f.get_name(1), "has_K2_edges-5_nodes-5--1.txt")
self.assertEqual(f.get_name(10), "has_K2_edges-5_nodes-5--10.txt")
f = File(self.directory, G=g, logger=self.logger, base="C5")
self.assertEqual(f.get_name(), "C5has_K2_edges-5_nodes-5.txt")
self.assertEqual(f.get_name(1), "C5has_K2_edges-5_nodes-5--1.txt")
self.assertEqual(f.get_name(10), "C5has_K2_edges-5_nodes-5--10.txt")
def testCompare(self):
claw = make_claw()
co_claw = make_co_claw()
f = File(self.directory, G=claw, logger=self.logger)
g = File(self.directory, G=claw, logger=self.logger)
self.assertEqual(g.compare(f), True)
self.assertEqual(f.compare(g), True)
g = File(self.directory, G=co_claw, logger=self.logger)
self.assertEqual(g.compare(f), False)
self.assertEqual(f.compare(g), False)
h = File(self.directory, G=make_cycle(4), logger=self.logger)
self.assertEqual(h.compare(f), False)
self.assertEqual(f.compare(h), False)
def setUp(self):
self.graph = make_cycle(5)
x = 5
y = 6
w = 7
self.graph.add_node(x)
self.graph.add_node(y)
self.graph.add_node(w)
self.graph.add_edge(1, x)
self.graph.add_edge(2, y)
self.graph.add_edge(3, y)
for i in range(0, 4):
self.graph.add_edge(i, w)