CoCalc -- Day9.sagews

Project: GBP-Hamiltonicity-2018

Views: ¹⁵²

load("conjecturing.py")
load("gt.sage")

loaded utilities
loaded invariants
loaded properties
loaded theorems
The truncated icosidodecahedral graph was not loaded. Caused by:
*Error: Numerical inconsistency is found.  Use the GMP exact arithmetic.
loaded graphs

Remember to load DIMACS and Sloane graphs if you want them

for g in graph_objects:
    if g.order()<20 and not g.is_bipartite() and g.is_perfect() and g.is_strongly_regular():
        print g.name()
        print g.graph6_string()
        g.show()

Octahedron
E}lw

k3_3 line graph
HRNcUdM

ce96
Gvz~r{

load("conjecturing.py")
load("gt.sage")

load("gt_precomputed_database.sage")
precomputed = precomputed_properties_for_conjecture()

k3 = graphs.CompleteGraph(3)
#[(is_clique)->(is_hamiltonian)] is TRUE
k3_4 = graphs.CompleteBipartiteGraph(3,4)
k5_5 = graphs.CompleteBipartiteGraph(5,5)
#(is_cycle)->(is_hamiltonian) is TRUE
k2 = graphs.CompleteGraph(2)
EH = graphs.EllinghamHorton54Graph()
#CLAIM: ((is_strongly_regular)&(is_bipartite))->(is_hamiltonian) is true for n>2
#NB presented a proof: we need to write this up!
pete = graphs.PetersenGraph()
c5 = graphs.CycleGraph(5)
fish = Graph([(0,1),(1,2),(2,3),(3,4),(4,5),(5,2),(2,0)])
c5_tail = graphs.CycleGraph(5)
#c5_tail.add_vertex()
c5_tail.add_edge(0,5)
bow_tie = Graph(5)
bow_tie.add_edges([(0,1),(1,2),(2,3),(3,4),(4,2),(2,0)])
c7 = graphs.CycleGraph(7)
c7_chord = graphs.CycleGraph(7)
c7_chord.add_edge(0,2)
glasses = Graph(7)
glasses.add_edges([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,3),(3,0)])
p3 = graphs.PathGraph(3)
k5 = graphs.CompleteGraph(5)

triangle_with_tail = graphs.CompleteGraph(3)
triangle_with_tail.add_edge(0,3)
blanusa2 = graphs.BlanusaSecondSnarkGraph()
duplex = Graph("Iv?GOKFY?")
heawood = graphs.HeawoodGraph()
frucht = graphs.FruchtGraph()
nb1 = Graph("Edj_")
tutte = graphs.TutteGraph()
pete = graphs.PetersenGraph()

robertson = graphs.RobertsonGraph()
hoffman = graphs.HoffmanGraph()
folkman = graphs.FolkmanGraph()
house = graphs.HouseGraph()

subdivided_k5 = graphs.CompleteGraph(5)
subdivided_k5.subdivide_edge((0,1),1)
subdivided_k5.show()
subdivided_k5.chromatic_index()

grid_2_3=graphs.Grid2dGraph(2,3)
grid_3_3=graphs.Grid2dGraph(3,3)
grid_3_3_3 = graphs.GridGraph([3,3,3])
k_4_6 = graphs.CompleteBipartiteGraph(4,6)
k3_4_edge=graphs.CompleteBipartiteGraph(3,4)
k3_4_edge.add_edge(0,1)

c5_chord_tail = graphs.CycleGraph(5)
c5_chord_tail.add_edge(0,2)
c5_chord_tail.add_vertex()
c5_chord_tail.add_edge(1,5)

ham1 = Graph("I~EGYCxyG")
ham2 = Graph("IjCKY{Tvg")
ham3 = Graph("Shk{\LP[mZnPDR^LaE{qz?GCIhgCcmL?C")

c8_chorded = graphs.CycleGraph(8)
c8_chorded.add_edge(0,3)
c8_chorded.add_edge(4,7)

def kite_necklace(k):
    #returns k kites joined head to tail
    if k==1:
        return Graph('DJk')
    g = graphs.CycleGraph(2*k)
    for i in [0..k-1]:
        g.subdivide_edge((0+2*i,1+2*i),1)
        g.add_edge(0+2*i,1+2*i)
        g.subdivide_edge((0+2*i,1+2*i),1)
        g.add_edge(2*k+2*i,2*k+2*i+1)
    return g

umbrella_4 = Graph("Ep{G")

5
5


#Run 6 of Day 8, rerun of earlier using precomputed database 
#Return to Sufficient Condition Conjectures
#using all graph objects so far
#adding some pre-coded known sufficient conditions: is_haggkvist_nicoghossian, is_fan, is_planar_transitive, is_generalized_dirac, is_lindquester

current_graph_objects = [k3,pete,c5,k5_5,k3_4,EH,c7_chord,bow_tie,k5,p3,glasses,fish,c5_tail,triangle_with_tail]

current_graph_objects.append(blanusa2)
current_graph_objects.append(frucht)
current_graph_objects.append(heawood)
current_graph_objects.append(duplex)
current_graph_objects.append(nb1)
current_graph_objects.append(tutte)
current_graph_objects.append(hoffman)
current_graph_objects.append(robertson)
current_graph_objects.append(folkman)
current_graph_objects.append(house)
current_graph_objects.append(subdivided_k5)
current_graph_objects.append(gould)
current_graph_objects.append(grid_2_3)
current_graph_objects.append(grid_3_3_3)
current_graph_objects.append(grid_3_3)
current_graph_objects.append(k_4_6)
current_graph_objects.append(k3_4_edge)
current_graph_objects.append(throwing)
current_graph_objects.append(c5_chord_tail)

#current_graph_objects.append(graphs.FosterGraph())
#order = 90
current_graph_objects.append(graphs.DesarguesGraph())
#current_graph_objects.append(graphs.Tutte12Cage())
#order = 126
#current_graph_objects.append(graphs.BiggsSmithGraph())
#order = 102
current_graph_objects.append(graphs.TutteCoxeterGraph())
current_graph_objects.append(k4)
current_graph_objects.append(graphs.CompleteBipartiteGraph(3,3))
current_graph_objects.append(graphs.PappusGraph())
current_graph_objects.append(graphs.CoxeterGraph())
current_graph_objects.append(graphs.DodecahedralGraph())
current_graph_objects.append(ham1)
current_graph_objects.append(ham2)
current_graph_objects.append(ham3)
current_graph_objects.append(c8_chorded)

property_of_interest = properties.index(Graph.is_hamiltonian)

theorem_s1 = lambda g: g.is_bipartite() and g.is_strongly_regular()
theorem_s2 = lambda g: g.is_circular_planar() and g.is_cartesian_product()

theorems = [Graph.is_cycle, Graph.is_clique, theorem_s1, is_ore, is_dirac, is_chvatal_erdos, theorem_s2,
is_haggkvist_nicoghossian, is_genghua_fan, is_planar_transitive, is_generalized_dirac, is_lindquester]

precomputed = precomputed_properties_for_conjecture()

conjs = propertyBasedConjecture(current_graph_objects, properties, property_of_interest, theory = theorems, time = 5, precomputed = precomputed, verbose=False, debug=True)
for c in conjs:
    print c

> Generation process was stopped by the conjecturing heuristic.
> Found 5 unlabeled trees.
> Found 27602 labeled trees.
> Found 2793 valid expressions.
((is_dart_free)->(is_planar_transitive))->(is_hamiltonian)
((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
((is_distance_regular)&(is_bipartite))->(is_hamiltonian)
((is_van_den_heuvel)&(is_circular_planar))->(is_hamiltonian)
((is_claw_free)&(is_van_den_heuvel))->(is_hamiltonian)
((~(is_weakly_chordal))&(is_eulerian))->(is_hamiltonian)

g = Graph("Ep{G")
g.show()

is_van_den_heuvel(g)

True

#Run 2 of Day 9, 
#adding CE to conjecture: ((is_van_den_heuvel)&(is_circular_planar))->(is_hamiltonian)
#graph is umbrella_4 = Graph("Ep{G")
#Return to Sufficient Condition Conjectures
#using all graph objects so far


current_graph_objects = [k3,pete,c5,k5_5,k3_4,EH,c7_chord,bow_tie,k5,p3,glasses,fish,c5_tail,triangle_with_tail]

current_graph_objects.append(blanusa2)
current_graph_objects.append(frucht)
current_graph_objects.append(heawood)
current_graph_objects.append(duplex)
current_graph_objects.append(nb1)
current_graph_objects.append(tutte)
current_graph_objects.append(hoffman)
current_graph_objects.append(robertson)
current_graph_objects.append(folkman)
current_graph_objects.append(house)
current_graph_objects.append(subdivided_k5)
current_graph_objects.append(gould)
current_graph_objects.append(grid_2_3)
current_graph_objects.append(grid_3_3_3)
current_graph_objects.append(grid_3_3)
current_graph_objects.append(k_4_6)
current_graph_objects.append(k3_4_edge)
current_graph_objects.append(throwing)
current_graph_objects.append(c5_chord_tail)

#current_graph_objects.append(graphs.FosterGraph())
#order = 90
current_graph_objects.append(graphs.DesarguesGraph())
#current_graph_objects.append(graphs.Tutte12Cage())
#order = 126
#current_graph_objects.append(graphs.BiggsSmithGraph())
#order = 102
current_graph_objects.append(graphs.TutteCoxeterGraph())
current_graph_objects.append(k4)
current_graph_objects.append(graphs.CompleteBipartiteGraph(3,3))
current_graph_objects.append(graphs.PappusGraph())
current_graph_objects.append(graphs.CoxeterGraph())
current_graph_objects.append(graphs.DodecahedralGraph())
current_graph_objects.append(ham1)
current_graph_objects.append(ham2)
current_graph_objects.append(ham3)
current_graph_objects.append(c8_chorded)
current_graph_objects.append(umbrella_4)

property_of_interest = properties.index(Graph.is_hamiltonian)

theorem_s1 = lambda g: g.is_bipartite() and g.is_strongly_regular()
theorem_s2 = lambda g: g.is_circular_planar() and g.is_cartesian_product()

theorems = [Graph.is_cycle, Graph.is_clique, theorem_s1, is_ore, is_dirac, is_chvatal_erdos, theorem_s2,
is_haggkvist_nicoghossian, is_genghua_fan, is_planar_transitive, is_generalized_dirac, is_lindquester]

precomputed = precomputed_properties_for_conjecture()

conjs = propertyBasedConjecture(current_graph_objects, properties, property_of_interest, theory = theorems, time = 5, precomputed = precomputed, verbose=False, debug=True)
for c in conjs:
    print c

> Generation process was stopped by the conjecturing heuristic.
> Found 5 unlabeled trees.
> Found 27602 labeled trees.
> Found 2664 valid expressions.
((is_planar_transitive)|(is_locally_connected))->(is_hamiltonian)
((is_distance_regular)&(is_bipartite))->(is_hamiltonian)
((is_claw_free)&(is_van_den_heuvel))->(is_hamiltonian)
((is_two_connected)&(is_circular_planar))->(is_hamiltonian)
((has_dart)&(is_two_connected))->(is_hamiltonian)
((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
((~(is_weakly_chordal))&(is_eulerian))->(is_hamiltonian)

#BEST OF CONJECTURES
#distance-regular & bipartite => hamiltonian
#distance-regular & perfect => hamiltonian
#planar-transitive => hamiltonian

#Run 3 of Day 9, necessary condition conjectures

current_graph_objects = [k3,pete,c5,k5_5,k3_4,EH,c7_chord,bow_tie,k5,p3,glasses,fish,c5_tail,triangle_with_tail]

current_graph_objects.append(blanusa2)
current_graph_objects.append(frucht)
current_graph_objects.append(heawood)
current_graph_objects.append(duplex)
current_graph_objects.append(nb1)
current_graph_objects.append(tutte)
current_graph_objects.append(hoffman)
current_graph_objects.append(robertson)
current_graph_objects.append(folkman)
current_graph_objects.append(house)
current_graph_objects.append(subdivided_k5)
current_graph_objects.append(gould)
current_graph_objects.append(grid_2_3)
current_graph_objects.append(grid_3_3_3)
current_graph_objects.append(grid_3_3)
current_graph_objects.append(k_4_6)
current_graph_objects.append(k3_4_edge)
current_graph_objects.append(throwing)
current_graph_objects.append(c5_chord_tail)

#current_graph_objects.append(graphs.FosterGraph())
#order = 90
current_graph_objects.append(graphs.DesarguesGraph())
#current_graph_objects.append(graphs.Tutte12Cage())
#order = 126
#current_graph_objects.append(graphs.BiggsSmithGraph())
#order = 102
current_graph_objects.append(graphs.TutteCoxeterGraph())
current_graph_objects.append(k4)
current_graph_objects.append(graphs.CompleteBipartiteGraph(3,3))
current_graph_objects.append(graphs.PappusGraph())
current_graph_objects.append(graphs.CoxeterGraph())
current_graph_objects.append(graphs.DodecahedralGraph())
current_graph_objects.append(ham1)
current_graph_objects.append(ham2)
current_graph_objects.append(ham3)
current_graph_objects.append(c8_chorded)
current_graph_objects.append(umbrella_4)

property_of_interest = properties.index(Graph.is_hamiltonian)

matching_robust = lambda g: matching_covered(g)
theorem_n1 = lambda g: not is_cubic(g) or is_class1(g)

theorems = [matching_robust, is_van_den_heuvel, theorem_n1, is_two_connected, alpha_leq_order_over_two]
#we're started with no knowledge of necessary conditions for hamiltonicity

conjs = propertyBasedConjecture(current_graph_objects, properties, property_of_interest, theory = theorems, sufficient=False)
for c in conjs:
    print c

(is_hamiltonian)->((order_leq_twice_max_degree)|(is_locally_bipartite))
(is_hamiltonian)->(((is_regular)->(is_kite_free))&(matching_covered))
(is_hamiltonian)->(((is_regular)->(is_kite_free))&(alpha_leq_order_over_two))
(is_hamiltonian)->((is_independence_irreducible)->(is_anti_tutte))
(is_hamiltonian)->((has_c4)|(has_radius_equal_diameter))
(is_hamiltonian)->(((is_eulerian)|(is_planar))|(has_lovasz_theta_equals_cc))

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in graphs(4):
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in graphs(5):
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in graphs(6):
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in graphs(7):
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in graphs(8):
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investiigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
for g in gris_van_den_heuvelnt:
    if g.is_connected() and g.is_regular() and is_heliotropic_plant(g) and not g.is_hamiltonian():
        print g.graph6_string()
        g.show()
        break

#investigate: ((is_heliotropic_plant)&(is_regular))->(is_hamiltonian)
#try random regular graphs

def rand_regular_connected(n,d):
    counter=0
    gnd = graphs.RandomRegular(d,n)
    while not gnd.is_connected():
        gnd = graphs.RandomRegular(d,n)
        counter=counter+1
        if counter==200:
            gnd=k3
            print "+"
    return gnd

def cruelWorld(runs,min_size,max_size):
    for i in [1..runs]:
        print '.',
        orde=randint(min_size,max_size)
        #p=random()
        #p=0.5
        d = randint(3,orde-1)
        while is_odd(orde*d):
            d = randint(3,orde-1)
        g = rand_regular_connected(orde,d)
        if is_van_den_heuvel(g) and not g.is_hamiltonian():
            print g.graph6.string()
            break

        """
        while g.is_hamiltonian():
            g.delete_edge(choice(g.hamilton_cycle().edges()))
        if g.order()>2 and g.is_connected():
            print ',',g.is_hamiltonian()
            #if not g.is_hamiltonian():
                #g=MakeHFree(g,graphs.CycleGraph(g.order()))
            if (is_van_den_heuvel(g) and is_claw_free(g)):
                print ',',
                #if (not g.is_hamiltonian()):
                print g.graph6_string()
                max_size=g.order()-1    
"""
cruelWorld(1000,3,100)

is_odd(5)

True

def rand_regular_connected(n,d):
    counter=0
    gnd = graphs.RandomRegular(d,n)
    while not gnd.is_connected():
        gnd = graphs.RandomRegular(d,n)
        counter=counter+1
        if counter==200:
            gnd=k3
            print "+"
    return gnd

def cruelWorld(runs,min_size,max_size):
    for i in [1..runs]:
        print '.',
        orde=randint(min_size,max_size)
        #p=random()
        #p=0.5
        d = randint(3,orde-1)
        while is_odd(orde*d):
            d = randint(3,orde-1)
        print (orde,d),    
        g = rand_regular_connected(orde,d)
        if is_van_den_heuvel(g) and not g.is_hamiltonian():
            print g.graph6.string()
            break

        """
        while g.is_hamiltonian():
            g.delete_edge(choice(g.hamilton_cycle().edges()))
        if g.order()>2 and g.is_connected():
            print ',',g.is_hamiltonian()
            #if not g.is_hamiltonian():
                #g=MakeHFree(g,graphs.CycleGraph(g.order()))
            if (is_van_den_heuvel(g) and is_claw_free(g)):
                print ',',
                #if (not g.is_hamiltonian()):
                print g.graph6_string()
                max_size=g.order()-1    
"""
cruelWorld(1000,3,100)

. (7, 6) . (74, 65) . (58, 25) . (69, 56) . (49, 18) . (16, 5) . (75, 16) . (97, 66) . (13, 12) . (46, 20) . (87, 28) . (17, 16) . (31, 10) . (66, 21) . (75, 36) . (41, 8) . (9, 8) . (23, 10) . (8, 3) . (46, 28) . (76, 12) . (92, 3) . (31, 12) . (54, 43) . (49, 28) . (67, 32) . (5, 4) . (54, 15) . (31, 6) . (96, 77) . (18, 11) . (80, 19) . (75, 48) . (52, 26) . (47, 28) . (74, 57) . (87, 84) . (57, 14) . (47, 4) . (97, 90) . (78, 67) . (88, 50) . (94, 68) . (4, 3) . (30, 14) . (19, 6) . (5, 4) . (45, 30) . (93, 36) . (19, 6) . (8, 5) . (94, 6) . (46, 21) . (42, 26) . (10, 4) . (43, 40) . (93, 68) . (99, 44) . (67, 50) . (84, 24) 

k5

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
NameError: name 'k5' is not defined

len(graph_objects)

585

for g in graph_objects:
    if g.is_gallai_tree():
        show(g)
        print g.graph6_string()

g=Graph("OwCW?CB???_Bw?F?_[W?~")

g.show()

p=g.plot()

p.save("gallai.png")

k4

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
NameError: name 'k4' is not defined

k4.plot().save("k4.png")

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
NameError: name 'k4' is not defined

for g in graph_objects:
    if g.is_strongly_regular():
        show(g)
        print g.graph6_string()

k3_3=graphs.CompleteBipartiteGraph(3,3)
k3_3.show()

k3_3.plot().save("k3_3.png")

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
NameError: name 'k3_3' is not defined

for g in graph_objects:
    if g.order()<21 and g.is_distance_regular() and not g.is_strongly_regular():
        show(g)
        print g.graph6_string()
        print g.name()

g=graphs.HexahedralGraph()
g.plot().save("cube.png")


for g in graph_objects:
    if g.order()<11 and is_complement_of_chordal(g):
        show(g)
        print g.graph6_string()
        print g.name()

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
NameError: name 'g' is not defined

for g in graph_objects:
    if g.order()<11 and g.is_planar() and  g.is_vertex_transitive():
        show(g)
        print g.graph6_string()
        print g.name()


graphs.OctahedralGraph().plot().save("octahedron.png")


len(properties)

148

len(graph_objects)

585


len(efficient_invariants)

127

len(intractable_invariants)

33

len(efficiently_computable_properties)

112

len(intractable_properties)

36

dimacs_graphs

[]

c6.plot().save("c6.png")

graphs.PetersenGraph().plot().save("petersen.png")

graphs.DodecahedralGraph().plot().save("dodecahedron.png")

for g in graph_objects:
    if  g.order()<11 and g.is_circular_planar() and  g.is_cartesian_product():
        show(g)
        print g.graph6_string()

Cl

GhCiKC

E`dg

g=Graph("E`dg").plot().save("cartesian.png")

for g in graph_objects:
    if g.order()>=11 and g.order()<1 and g.is_line_graph() and  g.is_bipartite():
        show(g)
        print g.graph6_string()

        print g.name()

distreg_not_stronglyreg16

graphs.PetersenGraph().is_vertex_transitive()

True

load_dimacs_graphs()

loaded graph -  keller4
loaded graph -  gen200_p0.9_44
loaded graph -  p_hat300-2
loaded graph -  p_hat300-3
loaded graph -  brock200_2
loaded graph -  keller5
loaded graph -  brock800_4
loaded graph -  C1000.9
loaded graph -  brock400_2
loaded graph -  p_hat1500-3
loaded graph -  brock400_4
loaded graph -  keller6
loaded graph -  brock200_4
loaded graph -  C2000.5
loaded graph -  MANN_a27
loaded graph -  C4000.5
loaded graph -  brock800_2
loaded graph -  gen200_p0.9_55
loaded graph -  DSJC500_5
loaded graph -  p_hat700-3

Error in lines 1-1
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
    flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
  File "<string>", line 53699, in load_dimacs_graphs
  File "/ext/sage/sage-8.4_1804/local/lib/python2.7/site-packages/sage/graphs/graph.py", line 1151, in __init__
    from_graph6(self, data)
  File "/ext/sage/sage-8.4_1804/local/lib/python2.7/site-packages/sage/graphs/graph_input.py", line 64, in from_graph6
    G._backend.add_edge(i, j, None, False)
  File "src/cysignals/signals.pyx", line 265, in cysignals.signals.python_check_interrupt
  File "src/cysignals/signals.pyx", line 98, in cysignals.signals.sig_raise_exception
KeyboardInterrupt

len(dimacs_graphs

36

g.cut

for g in graph_objects:
    if g.order()==5 and not is_two_connected(g):
        show(g)
        print g.graph6_string()
        print g.name()

Graph("DK{").plot().save("bow_tie.png")

for g in graph_objects:
    if g.order()<20  and is_complement_of_chordal(g) and not g.is_hamiltonian():
        show(g)
        print g.graph6_string()
        print g.name()

DyG
Bull graph

Cs
Claw graph

A_
alpha_critical_A_

Bg
p3

Ch
p4

Ds_
k1_4

IsaCCA?_?
k1_9

G?B~vo
k5_3

M{aCCA?_C?O?_?_??
s13e

N~~eeQoiCoM?Y?U?F??
starfish

C{
paw

DnC
dart

H??E@cN
ce6

Exi?
ce43

FWKH?
ce45

E?Bw
ce75

P?????????^~v~V~rzyZ~du{
ce81

J?Bzvrw}Fo?
ce116

L??F~z{~FwN_~?
ce125

M????B~~v}^w~o~o?
ce128

E~}?
k5pendant

DhO
fork

H}qdB@_
triangle_star

F?Azw
Elphick-Wocjan p.8

E?dg
double_fork

DBw
4-pan

DJk
kite with tail

F@J]o
chartrand fig 1.8 - F1

Ex{G
max_irregular_6

FnFwG
max_irregular_7

E@hW
barrus_332211c

EC\o
barrus_333221d

E?No
barrus_422211b

EANg
barrus_432221c

E?^o
barrus_432221d

E@vo
barrus_433222a

EIMw
barrus_433321a

E@^o
barrus_433321b

E?~o
barrus_442222a

E_lw
barrus_442222b

E@~o
barrus_443322a

EBxw
barrus_443331a

F@N~w
larson

G?rHx{
levit_1

Ep{G
umbrella_4

D|g
bus

E@~w
DaMNeD1

F@N]w
DaMNeD2

F?~vw
ce142

g = graphs.DodecahedralGraph()
g.show()

latex(g)

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%
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\Vertex[style={minimum size=1.0cm,draw=cv2,fill=cfv2,text=clv2,shape=circle},LabelOut=false,L=\hbox{$2$},x=0.9549cm,y=0.0cm]{v2}
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%
\Edge[lw=0.1cm,style={color=cv0v1,},](v0)(v1)
\Edge[lw=0.1cm,style={color=cv0v10,},](v0)(v10)
\Edge[lw=0.1cm,style={color=cv0v19,},](v0)(v19)
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\Edge[lw=0.1cm,style={color=cv17v18,},](v17)(v18)
\Edge[lw=0.1cm,style={color=cv18v19,},](v18)(v19)
%
\end{tikzpicture}