def all_maotrees_have_kblock(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# or d > 3k/2 - 1
k = int(ceil(2 * ((d+1) / 3.0)) - 1)
result = {}
for m in all_maos(g):
m_ = list(m)
t = maotree(g, m_)
found = False
for p in t.paths():
if len(p) >= k:
# print p
kblock = certify_non_kblock(g, p[-(k+1):], k)
if not kblock:
found = True
if not found:
result['m'] = m
result['t'] = t
break
if result:
result['g'] = g6
result['k'] = k
result['d'] = d
return result
def single_mao_kb1p32(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# or d > 3k/2 - 1
k = int(ceil(2 * ((d+1) / 3.0)) - 1)
result = mao_kblock(g, k+1, g.nodes_iter().next())
if result:
result['g'] = g6
result['k'] = k
result['d'] = d
return result
def single_ALL_mao_kp1b(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= k+1, take maximal k
k = d-1
if k < 2:
return
last = None
for l in all_maos(g):
if not certify_non_kblock(g, l[-(k+1):], k+1):
return
return {'g': g6, 'd': d, 'k': k}
def single_mao_kp1b(g6):
""" [Verm1] """
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= k+1, take maximal k
k = d-1
s = g.nodes_iter().next()
result = mao_kblock(g, k+1, s)
if result:
result['g'] = g6
result['k'] = k
result['d'] = d
return result
def single_kp1b(g6):
""" [Verm3] """
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= k+1, take maximal k
k = d-1
def chk():
for candidates in combinations(g.nodes_iter(),k+1):
if not certify_non_kblock(g, candidates, k+1):
return True
return False
if not chk():
return {'g':g6, 'd': d, 'k': k}
def single_mao_all_kp1b(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= k+1, take maximal k
k = d-1
s = g.nodes_iter().next()
m = mao(g, s)
for i in xrange(0, len(g)-(k+1)):
result = certify_non_kblock(g, m[i:i+k+1], k+1)
if not result:
return
# all are non-k+1-blocks
result['g'] = g6
result['k'] = k
result['d'] = d
return result
def single_all_mao_kp1b(g6):
""" [Verm2] """
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= k+1, take maximal k
k = d-1
starters = []
for s in g.nodes_iter():
result = mao_kblock(g, k+1, s)
# result = None if it is indeed a MAO
if not result:
starters.append(s)
# we found one, let's skip ahead
break
if not starters:
return {'g':g6, 'd':d, 'k':k}
def single_maos_kb1p32(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= 3k/2
# or d > 3k/2 - 1
k = int(2 * (d / 3.0))
starters = []
for s in g.nodes_iter():
result = mao_kblock(g, k+1, s)
# result = None if it is indeed a MAO
if not result:
starters.append(s)
# we found one, let's skip ahead
break
if not starters:
return {'g':g6, 'd':d, 'k':k}
def single_kb1p32(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# d >= 3k/2
# or d > 3k/2 - 1
k = int(2 * (d / 3.0))
if node_connectivity(g) >= k:
return
def chk():
for candidates in combinations(g.nodes_iter(),k+1):
if not certify_non_kblock(g, candidates, k+1):
return True
return False
if not chk():
return {'g':g6, 'k': k, 'd': d}
def maotree_all_kblock(g6):
g = parse_graph6(g6)
d = min(g.degree().viewvalues())
# or d > 3k/2 - 1
k = int(ceil(2 * ((d+1) / 3.0)) - 1)
m = mao(g,0)
t = maotree(g,m)
result = None
for p in t.paths():
if len(p) >= k:
# print p
result = certify_non_kblock(g, p[-(k+1):], k)
if result:
break
if result:
result['g'] = g6
result['k'] = k
result['d'] = d
return result
