def CliqueNumEqualsChromaticNum(G):
result = False
if (graph_clique_number(G) == chromatic_number(G)):
result = True
return result
def ChromaticNumberEqualsCLiqueNumber(G):
if(chromatic_number(G) == graph_clique_number(G)):
result = True
else:
result = False
return result
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 HoangConjecture(G):
V = G.nodes()
chi = ceil(len(V)/3)
if chi == chromatic_number(G):
result = True
else:
result = False
return result
def is_critical(self):
'''
a method that finds if the graph is is_critical
Parameters:
None
Returns:
True if graph is is_critical
False otherwise
'''
is_critical = True
nodes = self._g.nodes()
index = 0
chromatic = chromatic_number(self._g)
self.logger.info("Chromatic number of G is %d" %chromatic)
while is_critical and index < len(nodes):
g = self._g.copy()
g.remove_node(nodes[index])
check = chromatic_number(g)
if check != (chromatic -1):
self.logger.info(index)
self.logger.info("G is not critical")
is_critical = False
index += 1
return is_critical
