def random_planar_graph(n, m):
G = Graph()
for _v in xrange(n):
G.add_vertex()
Edges = get_maximal_planar_edges(G, n, 0)
for _i in xrange(m):
pos = random.randint(0, len(Edges) - 1)
G.add_edge(Edges[pos][0], Edges[pos][1])
del Edges[pos]
return G
def load_from_edge_list(strFileName, G = None):
if G is None: G = Graph()
with open(strFileName, 'r') as f:
lines = f.readlines()
if not G: G = Graph()
v_list = dict()
for line in lines:
if len(line) == 0 or line == '\n': continue
if line == "": continue
fields = line.split()
if not len(fields): continue
if fields[0] == 'e':
u = int(fields[1])
v = int(fields[2])
if u not in v_list: v_list[u] = G.add_vertex()
if v not in v_list: v_list[v] = G.add_vertex()
x, y = v_list[u], v_list[v]
G.add_edge(x, y)
return G
def octahedron():
G = Graph()
v, w, x, y, z1, z2 = (G.add_vertex() for i in xrange(6))
for i, j in pairwise((v, w, x, y, v)):
G.add_edge(i, j)
G.add_edge(i, z1)
G.add_edge(i, z2)
G.is_planar()
return G
def reduce_3sat_to_3col(instance, G = None):
"""reduces a 3sat instance to a graph 3-coloring instance
receives a graph G
for each clause (a,b,c)
gadget:
(-a)----(a)---(g1)
| \
| (g3)---(g4) (X)
| / | \ / |
(-b)----(b)---(g2) | (T) |
| / \ |
(-c)----(c)-------------(g5) (F)
X is adjacent to all variables
"""
G = Graph() if G is None else G
# add common gadget
G.add_named_vertex('T')
G.add_named_vertex('F')
G.add_named_vertex('X')
G.add_edge('T', 'F')
G.add_edge('F', 'X')
G.add_edge('X', 'T')
# add gadget for variables
variables = sorted(set([abs(v) for clause in instance for v in clause]))
for v in variables:
G.add_named_vertex(v)
G.add_named_vertex(-v)
G.add_edge('X', v)
G.add_edge('X', -v)
G.add_edge(v, -v)
G.set_vertex_index(max(variables) + 1)
# add the clause gadgets
for a, b, c in instance:
g1, g2, g3, g4, g5 = [G.add_vertex() for _i in range(5)]
# triangle 1,2,3
G.add_edge(g1, g2) # 1
G.add_edge(g2, g3) # 2
G.add_edge(g3, g1) # 3
# bridge betwen triangle 1,2,3T and 4,5,T
G.add_edge(g3, g4) # 4
# triangle 3,4,5
G.add_edge(g4, g5) # 5
G.add_edge(g5, 'T') # 6
G.add_edge('T', g4) # 7
# edges for clause a,b,c
G.add_edge(a, g1) # 8
G.add_edge(b, g2) # 9
G.add_edge(c, g5) # 10
return G
