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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Monopolarity
Definition:
Input: A graph
G
in this class.
Output: True iff
G
is monopolar.
Linear
(0,2)-colorable
(0,2)-colorable ∩ chordal
(0,2)-graph ∩ bipartite
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar ∩ chordal
1-DIR
1-bounded bipartite
(2,0)-colorable ∩ chordal
(2,2)-colorable ∩ chordal
2-bounded bipartite
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-leaf power
2-subdivision
2-subdivision ∩ planar
2-tree
2-tree ∩ probe interval
(2C
4
,3K
2
,C
6
,E,P
2
∪ P
4
,P
6
,X
25
,X
26
,X
27
,X
28
,X
29
,odd-cycle)-free
2K
1
-free
(2K
2
,3K
1
,C
4
,P
4
)-free
(2K
2
,3K
1
,P
3
)-free
(2K
2
,C
4
,C
5
,H,S
3
,X
160
,
X
159
,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,X
159
,X
160
,
H
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,S
3
,claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,S
3
,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,net)-free
(2K
2
,C
4
,C
5
,claw,diamond)-free
(2K
2
,C
4
,C
5
,co-claw,co-diamond)-free
(2K
2
,C
4
,C
5
,co-sun)-free
(2K
2
,C
4
,C
5
,sun)-free
(2K
2
,C
4
,C
5
)-free
(2K
2
,C
4
,P
4
,triangle)-free
(2K
2
,C
4
,P
4
)-free
(2K
2
,C
4
)-free
(2K
2
,C
5
,triangle)-free
(2K
2
,P
3
,triangle)-free
(2K
2
,P
3
)-free
2K
2
-free ∩ bipartite
(2K
3
,2P
3
,C
4
,K
3
∪ P
3
,P
4
)-free
(2K
3
,2P
3
,C
n+4
,K
3
∪ P
3
)-free
(2K
3
,C
n+4
)-free
(2P
3
,3K
2
,C
4
,C
5
,H,P
2
∪ P
4
,P
5
,S
3
,X
1
,X
160
,
X
159
,
X
161
,
X
162
,
X
46
,
X
70
,net,rising sun)-free
(2P
3
,C
4
,C
5
,P
5
,X
170
,
A
)-free
(2P
3
,C
4
,P
4
)-free
3-leaf power
3-tree
3-tree ∩ planar
(3K
1
,C
4
,C
5
)-free
(3K
1
,C
4
,
P
3
)-free
(3K
1
,C
5
,butterfly,diamond)-free
(3K
1
,P
3
)-free
(3K
2
,C
6
,P
7
,X
164
,X
165
,odd-cycle,sunlet
4
)-free
(3K
3
,C
n+4
)-free
(3P
3
,C
n+4
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,
A
)-free
3d grid
(4-fan,C
n+4
,K
5
- e,S
3
,X
100
,X
101
,X
102
,
H
,
K
3
∪ 2K
1
)-free
(4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
4-leaf power
5-leaf power
5-leaf power ∩ distance-hereditary
(6,1)-chordal ∩ bipartite
(6,2)-chordal ∩ bipartite
(A,T
2
,odd-cycle)-free
AC
AT-free ∩ bipartite
AT-free ∩ chordal
Apollonian network
B
0
-VPG ∩ bipartite
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
BW
3
-free ∩ modular
(C
4
,C
5
,C
6
,C
7
,C
8
,XC
11
,claw,diamond)-free
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free ∩ planar
(C
4
,C
6
,odd-cycle)-free
(C
4
,K
4
,claw,diamond)-free
(C
4
,P
4
,dart)-free
(C
4
,P
4
,diamond,paw)-free
(C
4
,P
4
)-free
(C
4
,
P
3
,triangle)-free
(C
4
,
P
3
)-free
(C
4
,claw,diamond)-free
C
4
-free ∩ C
6
-free ∩ bipartite
C
4
-free ∩ co-comparability
C
4
-free ∩ induced-hereditary pseudo-modular
(C
5
,C
6
∪ K
1
,C
7
,K
3,3
∪ K
1
,K
3,3
-e ∪ K
1
,
K
5
- e
,domino ∪ K
1
,triangle)-free
(C
5
,C
6
,P
6
,triangle)-free
(C
5
,co-butterfly,co-diamond,triangle)-free
C
6
-free ∩ modular
(C
n+4
,H)-free
(C
n+4
,K
4
)-free
(C
n+4
,P
5
,bull)-free
(C
n+4
,P
5
,claw,gem)-free
(C
n+4
,S
3
∪ K
1
,
X
103
,claw,eiffeltower,net ∪ K
1
)-free
(C
n+4
,S
3
∪ K
1
,claw,net)-free
(C
n+4
,S
3
,claw,net)-free
(C
n+4
,S
3
,net)-free
(C
n+4
,S
3
)-free
(C
n+4
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-free
(C
n+4
,T
2
,XF
2
n+1
)-free
(C
n+4
,T
2
,net)-free
(C
n+4
,X
102
,X
204
,
P
3
∪ 2K
1
,gem)-free
(C
n+4
,X
59
,longhorn)-free
(C
n+4
,XF
1
2n+3
,XF
6
2n+2
,
X
34
,
X
36
,co-XF
2
n+1
,co-XF
3
n
)-free
(C
n+4
,
K
3
∪ 3K
1
,dart,gem)-free
(C
n+4
,bull,dart,gem)-free
(C
n+4
,claw,gem)-free
(C
n+4
,claw,net)-free
(C
n+4
,claw)-free
(C
n+4
,dart,gem)-free
(C
n+4
,diamond)-free
(C
n+4
,gem)-free
(C
n+4
,odd-sun)-free
(C
n+4
,sun)-free
C
n+4
-free
(C
n+6
,odd-cycle)-free
Dilworth 1
(E,odd-cycle)-free
E-free ∩ bipartite
EPT ∩ chordal
F
n
grid
Helly chordal
Helly chordal ∩ clique-chordal
Hilbertian
(K
1,4
,odd-cycle)-free
(K
1,4
,odd-cycle)-free ∩ planar
K
2,3
-free ∩ hereditary modular
K
2
-free
K
3
-minor-free
(K
4
,claw,diamond)-free
(K
5
- e,S
3
,
3K
2
,
A
,
C
4
∪ 2K
1
,
E
,
P
2
∪ P
3
,
R
,claw,co-twin-house,odd-hole)-free
(K
5
- e,W
5
,
A
,
C
4
∪ 2K
1
,
P
2
∪ P
3
,
R
,claw,co-twin-C
5
,co-twin-house)-free
(K
5
- e,
A
,
C
4
∪ 2K
1
,
P
2
∪ P
3
,
R
,claw,co-twin-house,odd-hole)-free
NLCT-width 1
(P
3
,triangle)-free
P
3
-free
(P
4
,cycle)-free
(P
4
,triangle)-free
P
4
-free ∩ starlike
(P
5
,bull)-free ∩ interval
P
6
-free ∩ chordal bipartite
(P
7
,odd-cycle,star
1,2,3
,sunlet
4
)-free
(P
7
,odd-cycle,star
1,2,3
)-free
(P
7
,odd-cycle)-free
P
7
-free ∩ bipartite
PURE-2-DIR
(S
3
,
3K
2
,
E
,odd-hole)-free ∩ line
(S
3
,claw,net)-free ∩ chordal
(S
3
,net)-free ∩ chordal
(S
3
,net)-free ∩ split
S
3
-free ∩ chordal
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(T
2
,X
2
,X
3
,hole,triangle)-free
(T
2
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X
177
,odd-cycle)-free
(X
79
,X
80
)-free ∩ modular
(XC
11
,claw,diamond)-free
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
(XC
12
,cycle)-free
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(
P
3
,triangle)-free
τ
k
-perfect for all k >= 2
absolute bipartite retract
almost CIS
almost median
astral triple-free
b-perfect ∩ chordal
balanced ∩ chordal
balanced ∩ line
basic 4-leaf power
bi-cograph
biconvex
binary Hamming
binary tree
binary tree ∩ partial grid
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ distance-hereditary
bipartite ∩ girth>=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ grid intersection
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ module-composed
bipartite ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ unit grid intersection
bipartite ∩ weakly chordal
bipartite chain
bipartite permutation
bipartite tolerance
bisplit ∩ triangle-free
block
block duplicate
boxicity 1
caterpillar
chordal
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ co-comparability
chordal ∩ cograph
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ domination perfect
chordal ∩ domino
chordal ∩ dually chordal
chordal ∩ gem-free
chordal ∩ hamiltonian
chordal ∩ hamiltonian ∩ planar
chordal ∩ hereditary clique-Helly
chordal ∩ hereditary dominating pair
chordal ∩ irredundance perfect
chordal ∩ maximal planar
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ planar
chordal ∩ probe diamond-free
chordal ∩ proper circular arc
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∩ unit circular arc
chordal bipartite
circular convex bipartite
(claw ∪ 3K
1
,odd-cycle)-free
(claw,diamond,odd-hole)-free
(claw,diamond)-free
(claw,odd-cycle)-free
claw-free ∩ interval
clique graphs of interval
cluster
co-bithreshold ∩ split
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-probe threshold
co-threshold tolerance
co-trivially perfect ∩ trivially perfect
cograph ∩ interval
cograph ∩ split
comparability ∩ split
comparability graphs of arborescence orders
comparability graphs of posets of interval dimension 2, height 2
comparability graphs of threshold orders
complete
complete bipartite
complete split
convex
cubical
cycle-free
difference
directed path
disjoint union of stars
(domino,hole,odd-cycle)-free
domino-free ∩ modular
doubly chordal
(fork,odd-cycle)-free
grid
grid graph
grid graph ∩ maximum degree 3
gridline
half
half-disk Helly
hamiltonian ∩ interval
hamiltonian ∩ split
hereditary Helly
hereditary X-chordal
hereditary absolute bipartite retract
hereditary clique-Helly ∩ line ∩ perfect
hereditary disk-Helly
hereditary dually chordal
hereditary median
hereditary modular
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
homogeneously representable
hypercube
independent module-composed
indifference
indifference ∩ split
intersection graph of nested intervals
interval
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-path graph, fixed k
k-tree, fixed k
leaf power
leaf power ∩ min leaf power
line
line ∩ mock threshold
line ∩ perfect
line ∩ well covered
line graphs of acyclic multigraphs
line graphs of bipartite graphs
line graphs of planar cubic bipartite graphs
line graphs of triangle-free graphs
linear NLC-width 1
linear domino
linear domino ∩ maximum degree 4
linear interval
lobster
maximal outerplanar
maximum degree 1
median
median ∩ planar
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
monopolar
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
odd-cycle-free
partial 3d grid
partial cube
partial grid
perfect ∩ triangle-free
perfect elimination bipartite
permutation ∩ split
power-chordal
premedian
probe bipartite chain
probe block
probe complete
probe interval ∩ tree
probe interval bigraph
probe threshold ∩ split
proper chordal
proper interval
proper interval bigraph
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
quasi-threshold
restricted block duplicate
rigid circuit
rooted directed path
semi-median
solid grid graph
split
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
square of tree
star convex
starlike
starlike threshold
strictly chordal
strongly chordal
substar
superfragile
thick tree
threshold
tolerance ∩ tree
tolerance ∩ triangle-free
tree
tree convex
triad convex
triangulated
trivially perfect
undirected path
unit interval
unit interval bigraph
well-partitioned chordal
back to top
Polynomial
(1,2)-polar
1-bounded tripartite
(2,0)-colorable
2-connected ∩ (P
6
,claw)-free
2-threshold
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
,
H
,
K
1,4
,
X
85
)-free
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
,
H
,
X
85
)-free
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,3K
1
)-free
(2K
2
,4K
1
,C
5
,co-diamond)-free
(2K
2
,4K
1
,co-claw,co-diamond)-free
(2K
2
,5K
1
,C
5
,K
3
∪ 2K
1
,P
3
∪ 2K
1
,
C
6
,
C
7
,
C
8
,
K
1,4
,
K
5
- e
,claw ∪ K
1
,co-butterfly,co-cricket,co-dart,co-gem)-free
(2K
2
,A,C
5
,
2P
3
,
X
170
,house)-free
(2K
2
,A,H)-free
(2K
2
,C
5
,S
3
,X
159
,X
160
,X
161
,X
162
,X
46
,X
70
,
2P
3
,
3K
2
,
H
,
P
2
∪ P
4
,
X
1
,co-rising sun,house,net)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,C
5
,
C
6
,net)-free
(2K
2
,C
5
,
T
2
)-free
(2K
2
,C
5
)-free
(2K
2
,K
3,3
,K
3,3
+e,P
4
,
2P
3
)-free
(2K
2
,P
4
,
2P
3
)-free
(2K
2
,P
4
,co-dart)-free
(2K
2
,P
4
,co-diamond,co-paw)-free
(2K
2
,P
4
)-free
(2K
2
,
2P
3
,
C
6
)-free
(2K
2
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
(2K
2
,
C
6
,odd anti-cycle)-free
(2K
2
,
P
6
)-free
(2K
2
,
X
91
,co-claw)-free
(2K
2
,claw)-free
(2K
2
,co-claw,co-diamond)-free
(2K
2
,co-diamond)-free
(2K
2
,house)-free
(2K
2
,net)-free
(2K
2
,odd anti-hole)-free
2K
2
-free
2K
2
-free ∩ probe cograph
2K
2
-free ∩ probe trivially perfect
(2K
3
+ e,3K
1
,C
5
,
T
2
,
X
18
,
X
94
,co-domino)-free
(2K
3
+ e,5-pan,A,C
6
,E,K
3,3
-e,P
6
,R,X
166
,X
167
,X
169
,X
170
,X
171
,X
172
,X
18
,X
37
,X
45
,X
5
,X
58
,X
84
,X
95
,X
98
,
5-pan
,
A
,
C
6
,
E
,
P
6
,
R
,
X
166
,
X
167
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
37
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
98
,antenna,co-antenna,co-domino,co-fish,co-twin-C
5
,co-twin-house,domino,fish,twin-C
5
,twin-house)-free
(2K
3
+ e,A,C
5
,C
6
,E,H,K
3,3
-e,P
6
,R,S
3
,X
166
,X
167
,X
168
,X
169
,X
170
,X
171
,X
172
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,X
96
,X
98
,
A
,
C
6
,
E
,
H
,
P
6
,
R
,
X
166
,
X
167
,
X
168
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
96
,
X
98
,antenna,co-antenna,co-cross,co-domino,co-fish,co-twin-house,cross,domino,fish,net,twin-house)-free
(2K
3
+ e,A,C
5
,C
6
,E,K
3,3
-e,P
6
,R,X
166
,X
167
,X
169
,X
170
,X
171
,X
172
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,X
98
,
A
,
C
6
,
E
,
P
6
,
R
,
X
166
,
X
167
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
98
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K
3
+ e,C
5
,C
6
,P
6
,X
5
,
2P
4
,
A
,
C
6
,
C
7
,
E
,
P
7
,
R
,
X
1
,
X
103
,
X
5
,
X
58
,
X
84
,
X
98
,antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet
4
)-free
(2K
3
,2K
3
+ e,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,W
4
,X
84
,X
95
,
A
,
C
6
,
P
6
,
X
5
,
X
98
,butterfly,co-domino,co-fish,fish)-free
(2K
3
,2K
3
+ e,3K
1
,
A
,
H
,
T
2
,
X
18
,
X
45
,co-domino)-free
(2K
3
,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,X
84
,
3K
2
,
C
4
∪ P
2
,
C
6
,
P
2
∪ P
4
,
P
6
,
X
18
,
X
5
,co-antenna,co-domino,co-fish)-free
(2K
3
,3K
1
,
A
,
H
,
X
45
)-free
(2P
3
,3K
2
,C
4
∪ P
2
,C
6
,K
2,3
,P
6
,X
130
,X
132
,X
134
,X
152
,X
153
,X
154
,X
155
,X
156
,X
157
,X
158
,X
18
,X
84
,
X
11
,
X
127
,
X
128
,
X
129
,
X
131
,
X
133
,
X
135
,
X
136
,
X
137
,
X
138
,
X
139
,
X
140
,
X
141
,
X
142
,
X
143
,
X
144
,
X
145
,
X
146
,
X
147
,
X
148
,
X
149
,
X
150
,
X
151
,
X
30
,
X
35
,
X
46
,co-XF
1
2n+3
,co-XF
6
2n+3
,co-antenna,co-eiffeltower,co-longhorn,domino,fish,odd anti-hole)-free
(2P
3
,P
4
)-free
(2P
4
,A,C
5
,C
6
,C
7
,E,K
3,3
-e,P
7
,R,X
1
,X
103
,X
5
,X
58
,X
84
,X
98
,
C
6
,
P
6
,
X
5
,
sunlet
4
,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
(3K
1
,C
5
,K
3
∪ K
4
,
BW
3
,
K
3,4
-e
,
T
2
,
X
18
,
X
92
,
X
93
)-free
(3K
1
,C
5
,K
5
- e,
C
6
∪ K
1
,
C
7
,
K
3,3
∪ K
1
,
K
3,3
-e ∪ K
1
,
domino ∪ K
1
)-free
(3K
1
,C
5
,
C
6
,
P
6
)-free
(3K
1
,C
5
,
C
6
,
X
164
,
X
165
,
sunlet
4
)-free
(3K
1
,P
4
)-free
(3K
1
,
2P
3
)-free
(3K
1
,
3K
2
)-free
(3K
1
,
C
6
)-free
(3K
1
,
E
)-free
(3K
1
,
H
)-free
(3K
1
,
K
1,5
)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
2
∪ P
4
)-free
(3K
1
,
P
3
)-free
(3K
1
,
P
6
)-free
(3K
1
,
T
2
,
X
2
,
X
3
,anti-hole)-free
(3K
1
,
X
172
)-free
(3K
1
,
XC
12
)-free
(3K
1
,co-cross)-free
(3K
1
,co-fork)-free
(3K
1
,house)-free
(3K
1
,paw)-free
3K
1
-free
(3K
2
,A,C
4
∪ 2K
1
,E,P
2
∪ P
3
,R,
K
5
- e
,co-claw,net,odd anti-hole,twin-house)-free
(3K
2
,C
4
∪ P
2
,C
5
,C
6
,K
2
∪ K
3
,K
3,3
,K
3,3
+e,P
2
∪ P
4
,P
6
,X
18
,X
5
,
2P
3
,
C
6
,
C
7
,
X
84
,antenna,domino,fish)-free
(3K
2
,C
4
∪ P
2
,C
5
,P
2
∪ P
4
,P
5
,S
3
,X
1
,X
46
,X
70
,
3K
2
,
C
4
∪ P
2
,
P
2
∪ P
4
,
X
1
,
X
46
,
X
70
,co-fish,co-rising sun,fish,house,net,rising sun)-free
(3K
2
,C
5
,P
2
∪ P
4
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
,net)-free
(3K
2
,co-paw,odd anti-hole)-free
(3P
3
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,X
184
,X
185
,X
186
,X
187
,X
188
,X
189
,X
190
,X
191
,X
192
,X
193
,
5-pan
,
A
,
P
6
,co-twin-C
5
)-free
(4,0)-colorable
(4K
1
,C
7
,S
3
,X
175
,X
176
,X
42
,
X
36
,claw,co-antenna,net,odd anti-hole)-free
(4K
1
,C
7
,X
195
,X
196
,X
38
,X
39
,
W
5
,
X
194
,
X
86
,
X
88
,
X
89
,
X
90
,house)-free
(4K
1
,C
7
,X
38
,X
39
,
K
3,3
∪ K
1
,
W
4
∪ K
1
,
W
5
,
X
86
,
X
87
,
X
88
,
X
89
,
X
90
,butterfly ∪ K
1
,diamond)-free
(4K
1
,K
4
)-free
(4K
1
,P
4
)-free
(4K
1
,
C
n+4
)-free
(4K
1
,co-claw,co-diamond)-free
(4K
1
,gem)-free
(4K
1
,house)-free
(4K
1
,net)-free
(4K
1
,odd anti-hole,odd-hole)-free
4K
1
-free
(5,1)
(5,2)-chordal
(5,2)-crossing-chordal
(5-pan,T
2
,X
172
)-free
(5-pan,T
2
,X
172
)-free ∩ planar
5K
1
-free
(6,2)
6K
1
-free
(7,3)
7K
1
-free
(8,4)
(A,C
5
,C
6
,K
2
∪ K
3
,K
3,3
,K
3,3
+e,K
3,3
-e,P
6
,X
5
,X
98
,
2P
3
,
C
6
,
C
7
,
W
4
,
X
84
,
X
95
,co-butterfly,co-fish,domino,fish)-free
(A,C
5
,C
6
,P
6
,domino,house)-free
(A,C
5
,P
5
,
A
,house,parachute,parapluie)-free
(A,E,S
3
,X
1
,domino,hole,house,net,rising sun)-free
(A,P
6
,clique wheel,domino,hole,house)-free
(A,
3P
3
,
C
n+4
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,house)-free
AT-free ∩ claw-free
Berge ∩ claw-free
(C
4
∪ P
2
,C
5
,C
6
,K
2
∪ K
3
,K
2,3
,P
6
,W
4
,X
18
,X
5
,X
84
,
C
4
∪ P
2
,
C
6
,
P
6
,
W
4
,
X
18
,
X
5
,
X
84
,antenna,co-antenna,co-domino,co-fish,domino,fish)-free
(C
4
,P
5
)-free
(C
4
,X
91
,claw)-free
(C
5
,C
6
,C
7
,C
8
,P
8
,X
19
,X
20
,X
21
,X
22
,gem,house)-free
(C
5
,C
6
,P
6
,X
17
,X
18
,X
5
,X
98
,
C
6
,
P
6
,antenna,domino)-free
(C
5
,C
6
,P
6
,
C
6
,
P
6
,
X
17
,
X
18
,
X
5
,
X
98
,co-antenna,co-domino)-free
(C
5
,C
6
,P
6
,
C
6
,
P
6
)-free
(C
5
,K
2
∪ K
3
,K
2,3
,P,P
2
∪ P
3
,P
5
,
P
,
P
2
∪ P
3
,co-fork,fork,house)-free
(C
5
,P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(C
5
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P,P
5
,
P
,co-fork,fork,house)-free
(C
5
,P,P
5
,
P
,house)-free
(C
5
,P,P
5
,house)-free
(C
5
,P,co-fork,fork,gem,house)-free
(C
5
,P
5
,
A
,
C
6
,
P
6
,co-domino)-free
(C
5
,P
5
,
C
6
,
C
7
,
C
8
,
P
8
,
X
19
,
X
20
,
X
21
,
X
22
,co-gem)-free
(C
5
,P
5
,
P
,co-fork,co-gem,fork)-free
(C
5
,P
5
,
P
,house)-free
(C
5
,P
5
,
P
2
∪ P
3
)-free
(C
5
,P
5
,co-fish,fish,house)-free
(C
5
,P
5
,gem)-free
(C
5
,P
5
,house)-free
(C
5
,P
5
)-free
(C
5
,S
3
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
3K
2
,
P
2
∪ P
4
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free ∩ P
4
-tidy
(C
5
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
(C
6
,K
2
∪ K
3
,X
103
,X
37
,X
88
,X
90
,
C
n+4
∪ K
1
,
T
2
,
net ∪ K
1
,co-diamond,co-domino,co-eiffeltower,co-twin-C
5
)-free
(C
6
,P
6
,
P
6
,
X
10
,
X
11
,
X
12
,
X
13
,
X
14
,
X
15
,
X
5
,
X
6
,
X
7
,
X
8
,
X
9
,anti-hole,co-antenna)-free
(C
6
,
C
6
)-free murky
(C
n+4
∪ K
1
,C(n,k),W
4
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+4
∪ K
1
,C(n,k),X
42
,
T
2
,
X
2
,
X
3
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+4
∪ K
1
,S
3
∪ K
1
,X
42
,
T
2
,
X
2
,
X
3
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+4
∪ K
1
,S
3
∪ K
1
,X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+4
∪ K
1
,S
3
,W
4
,W
5
,
C
6
,claw,net)-free
(C
n+4
∪ K
1
,S
3
,W
4
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,XF
2
n+1
,XF
3
n
,XF
4
n
,anti-hole,co-XF
1
2n+3
,co-XF
5
2n+3
,co-XF
6
2n+2
)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,XF
2
n+1
,XF
3
n
,XF
4
n
,co-XF
1
2n+3
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd anti-hole)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
36
,XF
1
2n+3
,XF
2
n+1
,XF
3
n
,XF
4
n
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
36
,co-XF
1
2n+3
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd anti-hole)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
36
,XF
1
2n+3
,XF
2
n+1
,XF
3
n
,XF
4
n
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
36
,co-XF
1
2n+3
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd-hole)-free
(C
n+6
,X
37
,claw,co-antenna,net,sun)-free
Dilworth 2
Dilworth 3
(H,K
3
∪ 2K
1
,
C
n+4
,
K
5
- e
,
X
100
,
X
101
,
X
102
,co-4-fan,net)-free
(H,K
3
∪ 2K
1
,
C
n+4
,
K
5
- e
,co-4-fan,net)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDG-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly circular arc ∩ concave-round
Helly circular arc ∩ quasi-line
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
2
∪ K
3
,P
4
,butterfly)-free
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-free
(K
2
∪ K
3
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2
∪ K
3
,co-diamond)-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
2,3
,P,P
5
)-free
(K
2,3
,P,hole)-free
(K
2,3
,P
4
,co-butterfly)-free
(K
2,3
,P
5
)-free
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-free
(K
3,3
∪ K
1
,K
4
,W
4
∪ K
1
,W
5
,X
86
,X
87
,X
88
,X
89
,X
90
,
C
7
,
X
38
,
X
39
,
butterfly ∪ K
1
,co-diamond)-free
(K
3,3,3
,
C
n+4
)-free
(K
3,3
,K
3,3
+e,
2P
3
,
C
n+4
)-free
(K
3,3
,P
5
)-free
(K
3,3
,
C
n+4
)-free
(K
3,3
-e,P
5
,X
98
)-free
(K
3,3
-e,P
5
,X
99
)-free
(K
3,3
-e,P
5
)-free
(K
4,4
,P
5
)-free
(K
4
,P
4
)-free
(K
4
,P
5
,W
5
,X
194
,X
86
,X
88
,X
89
,X
90
,
C
7
,
X
195
,
X
196
,
X
38
,
X
39
)-free
(K
4
,P
5
)-free
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N
*
(P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(P,P
5
,
3K
2
,gem)-free
(P,P
5
,
P
,co-fork,fork,house)-free
(P,P
5
,co-fork)-free
(P,P
5
)-free
(P,
P
,co-fork,fork)-free
(P
2
∪ P
3
,P
3
∪ 2K
1
,X
188
,X
214
,
W
4
,
X
102
,
X
204
,
X
209
,
X
210
,
X
212
,
X
213
,
X
215
,
X
216
,
X
217
,
X
218
,
X
86
,co-gem)-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
(P
4
,
2P
3
)-free
(P
4
,co-cycle)-free
(P
4
,co-diamond,co-paw)-free
(P
4
,diamond,paw)-free
P
4
-extendible
P
4
-extendible ∩ P
4
-sparse
P
4
-free
P
4
-indifference
P
4
-laden
P
4
-lite
P
4
-reducible
P
4
-simplicial
P
4
-sparse
P
4
-tidy
P
4
-tidy ∩ (S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
P
4
-tidy ∩ balanced
P
4
-tidy ∩ hereditary clique-Helly ∩ perfect
P
4
-tidy ∩ perfect
(P
5
,S
3
,
A
,
E
,
X
1
,anti-hole,co-domino,co-rising sun,net)-free
(P
5
,S
3
,anti-hole,co-domino,co-gem)-free
(P
5
,X
82
,X
83
)-free
(P
5
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
,gem)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,anti-hole,co-bicycle,co-domino)-free
(P
5
,anti-hole,co-domino,co-gem)-free
(P
5
,anti-hole,co-domino,co-sun)-free
(P
5
,anti-hole,co-domino)-free
(P
5
,anti-hole,co-gem)-free
(P
5
,anti-hole)-free
(P
5
,bull,co-fork)-free
(P
5
,bull,house)-free
(P
5
,bull,odd anti-hole)-free
(P
5
,bull)-free
(P
5
,claw)-free
(P
5
,co-domino,co-gem)-free
(P
5
,co-fork,house)-free
(P
5
,co-fork)-free
(P
5
,cricket)-free
(P
5
,diamond)-free
(P
5
,fork,house)-free
(P
5
,fork)-free
(P
5
,gem)-free
(P
5
,house)-free
(P
5
,triangle)-free
P
5
-free
P
5
-free ∩ tripartite
P
5
-free ∩ weakly chordal
(P
6
,X
10
,X
11
,X
12
,X
13
,X
14
,X
15
,X
5
,X
6
,X
7
,X
8
,X
9
,
C
6
,
P
6
,antenna,hole)-free
(P
6
,claw)-free
PI
PI
*
(S
3
,
C
n+4
,
S
3
∪ K
1
,co-claw)-free
(S
3
,
C
n+4
,
T
2
)-free
(S
3
,
C
n+4
,co-claw,net)-free
(S
3
,
C
n+4
,co-claw)-free
(S
3
,
C
n+4
,net)-free
(S
3
,claw,net)-free
(S
3
,net)-free ∩ extended P
4
-sparse
(W
4
,claw,gem,odd-hole)-free
(W
4
,claw,gem)-free
(W
4
,claw)-free
Welsh-Powell opposition
(X
103
,
C
n+4
,
S
3
∪ K
1
,
net ∪ K
1
,co-claw,co-eiffeltower)-free
(X
12
,X
5
,X
95
,X
96
,X
97
,
X
12
,
X
5
,
X
95
,
X
96
,
X
97
,
claw ∪ triangle
,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X
34
,X
36
,XF
2
n+1
,XF
3
n
,
C
n+4
,co-XF
1
2n+3
,co-XF
6
2n+2
)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
(X
91
,claw)-free
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
(XC
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
XC
9
-free
(XF
1
2n+3
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
35
,
X
36
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,hole)-free
(XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(
2C
4
,
3K
2
,
C
6
,
E
,
P
2
∪ P
4
,
P
6
,
X
25
,
X
26
,
X
27
,
X
28
,
X
29
,odd anti-cycle)-free
(
3K
2
,
C
6
,
P
7
,
X
164
,
X
165
,
sunlet
4
,odd anti-cycle)-free
(
A
,
T
2
,odd anti-cycle)-free
(
C
n+3
∪ K
1
,co-diamond,co-paw)-free
(
C
n+4
,
H
)-free
(
C
n+4
,
T
2
,
X
31
,co-XF
2
n+1
,co-XF
3
n
)-free
(
C
n+4
,
T
2
,co-XF
2
n+1
)-free
(
C
n+4
,
X
59
,co-longhorn)-free
(
C
n+4
,bull,co-dart,co-gem)-free
(
C
n+4
,bull,house)-free
(
C
n+4
,co-claw,co-gem,house)-free
(
C
n+4
,co-claw,co-gem)-free
(
C
n+4
,co-claw)-free
(
C
n+4
,co-dart,co-gem)-free
(
C
n+4
,co-diamond)-free
(
C
n+4
,co-gem)-free
(
C
n+4
,co-sun)-free
(
C
n+4
,net)-free
(
C
n+4
,odd co-sun)-free
C
n+4
-free
(
C
n+6
,odd anti-cycle)-free
(
E
,odd anti-cycle)-free
(
K
1,4
,co-diamond)-free
(
K
1,4
,co-paw)-free
(
K
1,4
,odd anti-cycle)-free
(
P
,butterfly,fork,gem)-free
(
P
,fork,gem)-free
(
P
,fork,house)-free
(
P
,fork)-free
P
3
-free
(
P
7
,
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
P
7
,
star
1,2,3
,odd anti-cycle)-free
(
P
7
,odd anti-cycle)-free
(
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,even anti-hole,odd anti-cycle)-free
(
T
2
,co-cycle)-free
(
T
3
,
X
81
,co-cycle)-free
(
T
3
,co-cycle)-free
W
2n+3
-free
(
X
177
,odd anti-cycle)-free
(
X
37
,co-diamond,even anti-cycle)-free
(
XC
11
,co-claw,co-diamond)-free
(
XC
11
,odd anti-cycle)-free
XC
11
-free
(
XC
12
,co-cycle)-free
XC
12
-free
XC
13
-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
odd-cycle ∪ K
1
-free
(
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
star
1,2,3
,odd anti-cycle)-free
absolutely perfect
almost-split
alternately orientable ∩ co-comparability
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
b-perfect
biclique separable
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ split
bipolarizable
bithreshold
bitolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
brittle
(bull,co-fork,fork)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,fork)-free
(bull,hole,odd anti-hole)-free
(butterfly,claw)-free
charming
chordal ∪ co-chordal
chordal-perfect
circle graph with equator
circular arc ∩ co-bipartite
circular arc ∩ cograph
circular interval
(claw,co-claw)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ normal Helly circular arc
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
claw-free ∩ upper domination perfect
claw-free ∩ well covered
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
cliquewidth 2
co-2-subdivision
co-Gallai
co-HHD-free
co-Meyniel
co-Welsh-Powell opposition
co-β-perfect
co-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bounded tolerance
co-building-free
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
co-comparability
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 2
co-comparability graphs of posets of interval dimension d
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,even anti-cycle)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-forest-perfect
(co-fork,hole)-free
(co-fork,odd anti-cycle)-free
co-interval
co-interval ∩ cograph
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-leaf power
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
(co-paw,paw)-free
(co-paw,triangle)-free
co-paw-free
co-planar
co-probe cograph
co-proper interval bigraph
co-strongly chordal
co-tolerance
co-trapezoid
co-trivially perfect
cograph
cograph contraction
comparability ∩ distance-hereditary
comparability ∩ weakly chordal
comparability graphs of dimension 2 posets
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension 2, height 3
comparability graphs of semiorders
comparability graphs of series-parallel posets
complete multipartite
concave-round
containment graph of intervals
d-trapezoid
distance-hereditary
domination
domino
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
domishold
even anti-cycle-free
even-hole-free ∩ probe chordal
extended P
4
-laden
extended P
4
-reducible
extended P
4
-sparse
forest-perfect
(fork,house)-free
(fork,triangle)-free
fork-free
fuzzy circular interval
fuzzy linear interval
generalized strongly chordal
good
hereditary Matula perfect
hereditary N
*
-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary homogeneously orderable
hereditary sat
(hole,odd anti-hole)-free
hole-free
hole-free ∩ planar
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
intersection graphs of parallelograms (squares)
leaf power ∪ min leaf power
line graphs of bipartite multigraphs
line graphs of multigraphs without triangles
linear cliquewidth 2
matrogenic
matroidal
maxibrittle
maximal planar
middle
min leaf power
mock threshold
module-composed
multitolerance
odd anti-cycle-free
parallelepiped
perfect connected-dominant
permutation
probe HHDS-free
probe P
4
-reducible
probe bipartite distance-hereditary
probe chordal ∩ weakly chordal
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe proper interval
probe ptolemaic
probe strongly chordal
probe threshold
probe trivially perfect
probe unit interval
proper Helly circular arc
proper circular arc
proper tolerance
quasi-brittle
quasi-line
quasitriangulated
semi-P
4
-sparse
semicircular
semiperfectly orderable
split-perfect
strict 2-threshold
strong tree-cograph
strongly orderable
sun-free ∩ weakly chordal
superbrittle
threshold signed
threshold tolerance
tolerance
trapezoepiped
trapezoid
tree-cograph
tree-perfect
unit Helly circular arc
unit circular arc
unit tolerance
weak bipolarizable
weakly chordal
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
(0,3)-colorable
(1,2)-split
1-string
2-SEG
2-circular arc
2-circular track
2-interval
2-track
(2K
3
+ e,
X
98
,house)-free
(2K
3
+ e,
X
99
,house)-free
(2K
3
+ e,house)-free
(2K
3
,2K
3
+ e,
A
,
H
,
X
45
,
XZ
5
,co-domino)-free
(2K
3
,X
42
,
A
,
H
,
X
45
,
X
46
,
X
47
,
X
48
,
X
49
,
X
50
,
X
51
,
X
52
,
X
53
,
X
54
,
X
55
,
X
56
,
X
57
)-free
(2K
3
,house)-free
(2K
4
,house)-free
3-DIR
3-DIR contact
3-circular track
3-interval
3-mino
3-track
4-colorable
(4-fan,K
1,4
,W
4
,W
5
,
A ∪ K
1
,
co-fork ∪ K
1
,
gem ∪ K
1
,
net ∪ K
1
)-free
(5,2)
5-colorable
6-colorable
B
1
-CPG
B
1
-CPG ∩ triangle-free
B
1
-VCPG
B
1
-VPG
B
2
-VPG
B
3
-VPG
(BW
3
,W
5
,W
7
,X
103
,X
104
,X
105
,X
106
,X
107
,X
108
,X
109
,X
110
,X
111
,X
112
,X
113
,X
114
,X
115
,X
116
,X
117
,X
118
,X
119
,X
120
,X
121
,X
122
,X
123
,X
124
,X
125
,X
126
,X
53
,X
88
,
C
6
,
C
8
,
T
2
,
X
3
)-free
BW
3
-free
B
k
-VPG
Bouchet
(C
4
,C
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free ∩ planar
(C
4
,C
5
,C
6
,C
7
,C
8
)-free
(C
4
,C
5
,C
6
,C
7
,C
8
)-free ∩ maximum degree 3 ∩ planar
(C
4
,C
5
,C
6
,S
3
)-free
(C
4
,C
5
)-free
(C
4
,S
3
)-free
(C
4
,
A
,
H
)-free
C
4
-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free
(C
5
,house)-free
C
5
-free
(C
6
,
C
6
)-free
(C
6
,house)-free
C
6
-free
(C
7
,odd anti-hole)-free
CONV
CPG
Helly 2-acyclic subtree
(K
1,4
,diamond)-free
(K
1,4
,paw)-free
K
1,4
-free
(K
1,5
,triangle)-free
(K
2
∪ K
3
,
P
,house)-free
(K
2
∪ K
3
,house)-free
K
2
∪ K
3
-free
K
2,3
-free
(K
3
∪ 2K
1
,
K
3
∪ 2K
1
,bull,co-cricket,co-dart,cricket,dart)-free
(K
3
∪ P
3
,
C
6
,
P
,
P
7
,
X
37
,
X
41
)-free
(K
3,3
,K
5
)-minor-free
(K
4
,S
3
)-free
K
4
-free
K
4
-free ∩ map
K
4
-free ∩ planar
K
5
-free
K
6
-free
K
7
-free
P-free
P
4
-bipartite
(S
3
,S
4
,net)-free
(S
3
,
3K
2
,
E
,
P
2
∪ P
4
)-free
(S
3
,
C
n+6
,
X
37
,antenna,co-claw,co-sun)-free
(S
3
,co-claw,net)-free
(S
3
,co-claw)-free
(S
3
,net)-free
(S
3
,net)-free ∩ sun-free
S
3
-free
SEG
VPG
W
2n+3
-free
(W
4
,W
5
,butterfly)-free
(W
4
,X
102
,X
204
,X
209
,X
210
,X
212
,X
213
,X
214
,X
215
,X
216
,X
217
,X
218
,X
86
,
P
2
∪ P
3
,
P
3
∪ 2K
1
,
X
188
,gem)-free
(W
4
,gem)-free
W
n+4
-free
(X
30
,XZ
1
,XZ
4
,longhorn)-free
(X
38
,gem,house)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free
(X
79
,X
80
)-free
XC
10
-free
(XC
12
,triangle)-free
(XC
12
,triangle)-free ∩ planar
XC
13
-free
cal P
3
-perfect
2P
3
-free
(
5-pan
,
T
2
,
X
172
)-free
(
A
,
P
6
,co-domino)-free
BW
3
-free
C
6
-free
(
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
35
,
X
36
,
X
37
,
X
38
,
X
39
,
X
40
,
X
41
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
)-free
C
n+6
-free
C
n+7
-free
(
E
,
P
)-free
E
-free
(
K
1,4
,
P
,co-fork,house)-free
(
K
1,4
,house)-free
K
1,4
-free
K
2
∪ claw
-free
(
P
,
P
7
)-free
(
P
,
P
8
)-free
(
P
,
T
2
)-free
(
P
,
star
1,2,3
)-free
(
P
,co-star
1,2,4
)-free
(
P
,co-star
1,2,5
)-free
(
P
,house)-free
P
-free
P
2
∪ P
4
-free
(
P
6
,
X
30
,
X
8
)-free
(
P
6
,co-claw)-free
P
6
-free
P
7
-free
(
X
30
,
XZ
1
,
XZ
4
,co-longhorn)-free
(
X
79
,
X
80
)-free
(
X
82
,
X
83
,house)-free
(
X
91
,co-claw)-free
(n+4)-pan
-free
alternation
anti-hole-free
apex
biplanar
book thickness 2
building-free
(bull,co-fork)-free
(bull,house)-free
bull-free
(butterfly,gem)-free
caterpillar arboricity <= 2
clique graphs
clique-Helly
(co-claw,house)-free
co-claw-free
(co-cricket,house)-free
co-domino-free
(co-fork,house)-free
co-fork-free
co-sun-free
coin
(cross,triangle)-free
diamond-free
disk
disk contact
(domino,gem,house)-free
domino-free
even anti-hole-free
gem-free
genus 0
genus 1
hereditary clique-Helly
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
house-free
k-DIR
k-SEG
line graphs of Helly hypergraphs of rank 3
line graphs of linear hypergraphs of rank 3
linear arboricity <= 2
locally bipartite
locally chordal
locally split
map
maximal clique irreducible
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
neighbourhood chordal
neighbourhood-Helly
net-free
odd anti-hole-free
odd co-sun-free
odd-sun-free
partial bar visibility
partial rectangle visibility
paw-free
perfect cochromatic
planar
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe diamond-free
rectangle visibility
split-neighbourhood
strictly clique irreducible
string
subhamiltonian
sun-free
thickness <= 2
toroidal
triangle contact
triangle-free
tripartite
unit 2-circular track
unit 2-track
unit 3-circular track
unit 3-track
weak bar visibility
weak rectangle visibility
back to top
coNP-complete
back to top
Open
back to top
Unknown to ISGCI
(0,2)-graph
(1,2)-colorable
(2,2)-colorable
(2,2)-interval
2-DIR
2-connected
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-edge-connected
2-outerplanar
2-split
2-split ∩ perfect
2-strongly regular
2-strongly regular ∩ planar
2-terminal series-parallel
2-thin
(2K
3
+ e,A,C
5
,C
6
,E,H,K
3,3
-e,R,X
168
,X
171
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,
A
,
C
6
,
E
,
H
,
R
,
X
168
,
X
171
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2P
3
,C
4
,C
6
)-free
(2P
3
,triangle)-free
2P
3
-free
3-Helly
(3K
2
,C
5
,C
7
,P
2
∪ P
4
,X
173
,
X
11
,net)-free
(3K
2
,C
5
,P
2
∪ P
4
,net)-free
(3K
2
,E,P
2
∪ P
4
,net,odd anti-hole,odd-hole)-free
(3K
2
,E,P
2
∪ P
4
,net)-free
(3K
2
,E,net,odd anti-hole)-free
(3K
2
,
P
,co-gem,house)-free
(3K
2
,triangle)-free
4-regular
4-regular ∩ hamiltonian
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
(5-pan,A,P
6
,X
186
,
3P
3
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,
X
184
,
X
185
,
X
187
,
X
188
,
X
189
,
X
190
,
X
191
,
X
192
,
X
193
,house,twin-C
5
)-free
5-regular
5-regular ∩ hamiltonian
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,1)-chordal
(6,1)-even-chordal
(6,2)-chordal
(6,3)
(6-fan,C
4
∪ P
2
,C
5
,C
6
∪ K
1
,C
7
,K
2
∪ K
3
,K
2,3
,P
2
∪ P
4
,W
4
∪ K
1
,W
6
,X
132
,X
169
,X
176
,X
18
,X
197
,X
198
,X
199
,X
200
,X
201
,X
202
,X
35
,X
84
,
C
4
∪ P
2
,
C
6
∪ K
1
,
C
7
,
P
2
∪ P
4
,
W
4
∪ K
1
,
W
6
,
X
132
,
X
169
,
X
176
,
X
18
,
X
197
,
X
198
,
X
199
,
X
200
,
X
201
,
X
35
,
X
84
,
butterfly ∪ K
1
,butterfly ∪ K
1
,co-6-fan,co-fish,fish)-free
(7,4)
(7,5)
(9,6)
(A ∪ K
1
,
K
1,4
,
W
4
,
W
5
,co-4-fan,co-fork ∪ K
1
,gem ∪ K
1
,net ∪ K
1
)-free
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,
W
5
,co-claw,twin-C
5
,twin-house)-free
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,co-claw,odd anti-hole,twin-house)-free
(A,H,K
3,3
,K
3,3
-e,T
2
,X
18
,X
45
,domino,triangle)-free
(A,H,K
3,3
,K
3,3
-e,X
45
,XZ
5
,domino)-free
(A,H,K
3,3
,X
45
,X
46
,X
47
,X
48
,X
49
,X
50
,X
51
,X
52
,X
53
,X
54
,X
55
,X
56
,X
57
,
X
42
)-free
(A,H,K
3,3
,X
45
,triangle)-free
(A,P
6
,domino)-free
AT-free
B
0
-CPG
B
0
-VPG
B
0
-VPG ∩ triangle-free
(BW
3
,C
5
,K
3,4
,K
3,4
-e,T
2
,X
18
,X
92
,X
93
,triangle)-free
Berge
Berge ∩ bull-free
Birkhoff
(C
4
,C
5
,C
6
,C
7
,C
8
,H,K
1,4
,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,X
85
,triangle)-free ∩ K
1,4
-free
(C
4
,C
5
,K
4
,diamond)-free
(C
4
,C
5
,K
4
,diamond)-free ∩ planar
(C
4
,C
5
,T
2
)-free
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
(C
4
,P
6
)-free
(C
4
,co-claw)-free
(C
4
,diamond)-free
(C
4
,odd-hole)-free
(C
4
,triangle)-free
(C
4
,triangle)-free ∩ planar
C
4
-free ∩ odd-signable
C
4
-free ∩ perfect
(C
5
,C
6
,X
164
,X
165
,sunlet
4
,triangle)-free
(C
5
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-free
(C
5
,P,
P
,bull,co-fork,gem,house)-free
(C
5
,P
2
∪ P
3
,house)-free
(C
5
,P
6
,
P
6
)-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free ∩ co-line
(C
5
,bull,co-gem,gem)-free
(C
5
,co-gem,gem)-free
(C
5
,co-gem,house)-free
(C
6
,C
8
,T
2
,X
3
,
BW
3
,
W
5
,
W
7
,
X
103
,
X
105
,
X
106
,
X
107
,
X
108
,
X
109
,
X
110
,
X
111
,
X
112
,
X
113
,
X
114
,
X
115
,
X
116
,
X
117
,
X
118
,
X
119
,
X
120
,
X
121
,
X
122
,
X
123
,
X
124
,
X
125
,
X
126
,
X
53
,
X
88
,co-X
104
)-free
(C
6
,K
2
∪ K
3
,X
37
,X
90
,
C
n+4
∪ K
1
,
T
2
,
W
n+4
,
X
31
,co-XF
2
n+1
,co-XF
3
n
,co-domino,co-twin-C
5
)-free
(C
6
,K
3,3
+e,P,P
7
,X
37
,X
41
)-free
(C
6
,S
3
,
C
n+4
∪ K
1
,
W
4
,
W
5
,co-claw,net)-free
(C
6
,triangle)-free
CIS
(C
n+3
∪ K
1
,diamond,paw)-free
(C
n+4
∪ K
1
,K
2,3
,T
2
,W
n+4
,X
31
,XF
2
n+1
,XF
3
n
,
C
6
,
X
37
,
X
90
,domino,twin-C
5
)-free
(C
n+4
∪ K
1
,K
2,3
,T
2
,
C
6
,
X
103
,
X
37
,
X
88
,
X
90
,diamond,domino,eiffeltower,net ∪ K
1
,twin-C
5
)-free
(C
n+4
∪ K
1
,K
2,3
,T
2
,
X
90
,domino,paw,twin-C
5
)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,X
37
,X
38
,X
39
,X
40
,X
41
,XF
2
n+1
,XF
3
n
,XF
4
n
)-free
C
n+6
-free
C
n+7
-free
D
Delaunay
Deza
Dilworth 4
(E,P)-free
(E,triangle)-free
E-free
E-free ∩ planar
EPT
Gabriel
Gallai
Gallai-perfect
(H,triangle)-free
Halin
Hamilton-connected
Hamming
Helly
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly circle
Helly circular arc
Helly circular arc ∩ (
C
7
,odd-hole)-free
Helly circular arc ∩ perfect
Helly circular arc ∩ self-clique
Helly subtree
H
n,q
grid
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
(K
2
∪ K
3
,X
11
,X
127
,X
128
,X
129
,X
131
,X
133
,X
135
,X
136
,X
137
,X
138
,X
139
,X
140
,X
141
,X
142
,X
143
,X
144
,X
145
,X
146
,X
147
,X
148
,X
149
,X
150
,X
151
,X
30
,X
35
,X
46
,XF
1
2n+3
,XF
6
2n+3
,
2P
3
,
3K
2
,
C
4
∪ P
2
,
C
6
,
P
6
,
X
130
,
X
132
,
X
134
,
X
152
,
X
153
,
X
154
,
X
155
,
X
156
,
X
157
,
X
158
,
X
18
,
X
84
,antenna,co-domino,co-fish,eiffeltower,longhorn,odd-hole)-free
(K
2
∪ K
3
,
P
,anti-hole)-free
(K
2
∪ claw,triangle)-free
K
2
∪ claw-free
(K
2,3
,K
4
)-minor-free
(K
2,3
,X
37
,X
38
,diamond,domino,house,twin-C
5
)-free
(K
2,3
,diamond)-free
(K
2,3
,diamond)-free ∩ weakly modular
(K
4
,S
3
,X
36
,
C
7
,
X
175
,
X
176
,
X
42
,antenna,co-claw,net,odd-hole)-free
(K
4
,co-gem)-free
(K
4
,odd anti-hole,odd-hole)-free
(K
4
,odd anti-hole,odd-hole)-free ∩ dually chordal
K
4
-free ∩ dually chordal ∩ perfect
K
4
-free ∩ perfect
K
4
-minor-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
Laman
Laman ∩ planar
Matula perfect
Meyniel
Mycielski
N
*
-perfect
(P,P
7
)-free
(P,P
8
)-free
(P,T
2
)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-fork)-free
(P,co-gem,house)-free
(P,star
1,2,3
)-free
(P,star
1,2,4
)-free
(P,star
1,2,5
)-free
(P
2
∪ P
3
,house)-free
(P
2
∪ P
4
,triangle)-free
P
2
∪ P
4
-free
P
4
-brittle
P
4
-comparability
(P
6
,X
30
,X
8
)-free
(P
6
,triangle)-free
P
6
-free
P
6
-free ∩ tripartite
P
7
-free
PURE-3-DIR
PURE-k-DIR
Raspail
(S
3
,T
2
,X
2
,X
3
,
C
n+4
∪ K
1
,
C(n,k)
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,T
2
,X
2
,X
3
,
C
n+4
∪ K
1
,
S
3
∪ K
1
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,T
2
,X
205
,X
206
,X
207
,X
208
,
C
n+4
∪ K
1
,
S
3
∪ K
1
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,T
2
,X
205
,X
206
,X
207
,X
208
,
X
42
)-free
(S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
(S
3
,
3K
2
,
E
,odd-hole)-free
(S
3
,
C
n+4
∪ K
1
,
C(n,k)
,
W
4
,even-hole,odd-cycle ∪ K
1
)-free
Urquhart
V-perfect
(W
4
,gem)-free ∩ short-chorded
Welsh-Powell perfect
(X
172
,triangle)-free
(X
37
,diamond,even-cycle)-free
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(XF
1
2n+3
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
35
,
X
36
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,odd-hole)-free
β-perfect
cal C(G)-perfect
(
3K
2
,odd-hole,paw)-free
(
C
7
,odd-hole)-free
(
W
4
,
W
5
,co-butterfly)-free
(
W
4
,co-claw,co-gem,odd anti-hole)-free
(
W
4
,co-claw,co-gem)-free
(
W
4
,co-claw)-free
(
W
4
,co-gem)-free
W
n+4
-free
XC
10
-free
absolute reflexive retract
absorbantly perfect
all-4-simplicial
almost claw-free
almost tree (1)
alternately colourable
alternately orientable
(anti-hole,bull,odd-hole)-free
(anti-hole,odd-hole)-free
balanced
balanced 2-interval
balanced ∩ co-line
balanced ∩ paw-free
bar visibility
basic perfect
biclique-Helly
bigeodetic
bip
*
bipartable
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ double split ∪ line graphs of bipartite graphs
bisplit
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
boxicity 2
bridged
bridged ∩ clique-Helly
building-free ∩ even-signable
building-free ∩ odd-signable
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
cactus
circle
circle ∩ diamond-free
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular arc
circular arc ∩ clique-Helly
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular perfect
circular permutation
circular strip
circular trapezoid
clique separable
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-Helly ∩ dismantlable ∩ reflexive
clique-chordal
clique-perfect
clique-perfect ∩ triangle-free
cliquewidth 3
cliquewidth 4
co-Matula perfect
co-P
4
-brittle
co-Welsh-Powell perfect
co-biclique separable
(co-butterfly,co-claw)-free
(co-butterfly,co-gem)-free
co-circular perfect
(co-claw,odd anti-hole,odd-hole)-free
(co-claw,odd anti-hole)-free
(co-claw,odd-hole)-free
co-comparability ∪ comparability
(co-gem,gem)-free
(co-gem,house)-free
co-gem-free
co-hereditary clique-Helly
co-interval filament
co-interval mixed
co-line
co-perfectly orderable
co-quasi-line
co-unipolar
co-unipolar ∪ unipolar
comparability
comparability graphs of dimension 3 posets
comparability graphs of dimension 4 posets
comparability graphs of dimension d posets
comparability graphs of posets of interval dimension d
complete Hamming
containment graph of circles
containment graphs
containment graphs of circular arcs
convex-round
cop-win
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cycle-bicolorable
diametral path
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free ∩ perfect
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
double split
doubled
dually chordal
dually chordal ∩ tripartite
edge regular
equimatchable
even-cycle-free
even-hole-free
even-signable
frame hereditary dominating pair
fully cycle extendable
generalized split
generically minimally rigid
geodetic
girth>=9
graceful
grid intersection
hamiltonian
hamiltonian ∩ planar
harmonious
hereditary biclique-Helly
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary clique-Helly ∩ self-clique
hereditary dismantlable
hereditary dominating pair
hereditary open-neighbourhood-Helly
hereditary weakly modular
homogeneously orderable
homothetic triangle contact
i-triangulated
induced-hereditary pseudo-modular
interval enumerable
interval filament
interval regular
interval regular of diameter 2
irredundance perfect
irredundance perfect with ir(G)=2
irredundance perfect with ir(G)<= 4
isometric-HH-free
isometric-hereditary pseudo-modular
k-outerplanar
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
kernel solvable
line perfect
linearly convex triangular grid graph
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
locally perfect
max-tolerance
minimally imperfect
murky
(n+4)-pan-free
nK
2
-free, fixed n
nP
3
-free, fixed n
nearly bipartite
neighbourhood perfect
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
neighbourhood-Helly ∩ triangle-free
normal
normal Helly circular arc
normal circular arc
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-cycle ∪ K
1
-free
(odd-hole,paw)-free
odd-hole-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable
odd-signable ∩ triangle-free
open-neighbourhood-Helly
opposition
outer-string
outerplanar
overlap
(p,q)-colorable
(p,q)-split
(p,q<=2)-colorable
p-connected
p-tree
pairwise compatibility
parity
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 4-tree
partial k-tree, fixed k
partitionable
partner-limited
path orderable
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
planar ∩ strongly regular
polar
polyhedral
preperfect
probe AT-free
probe Gallai
probe Meyniel
probe P
4
-sparse
probe chordal
probe chordal bipartite
probe co-bipartite
probe co-comparability
probe comparability
probe permutation
probe split
pseudo-median
pseudo-modular
(q, q-3), fixed q>= 7
(q,q-4), fixed q
(q,t)
quasi-Meyniel
quasi-median
quasi-parity
rectagraph
rectangle intersection
reflexive
relative neighbourhood graph
self-clique
self-complementary
semi-square intersection
series-parallel
short-chorded
skeletal
slender
slightly triangulated
slim
solid triangular grid graph
spider graph
strict B
1
-VCPG
strict quasi-parity
strong asteroid free
strong domination perfect
strongly 3-colorable
strongly circular perfect
strongly even-signable
strongly odd-signable
strongly perfect
strongly regular
subtree filament
subtree overlap
superperfect
totally unimodular
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triangular grid graph
unbreakable
unicyclic
unigraph
unimodular
unipolar
unit 2-circular arc
unit 2-interval
unit 3-interval
unit Helly circle
unit bar visibility
unit disk
unit grid intersection
universally signable
upper domination perfect
upper irredundance perfect
very strongly perfect
visibility
walk regular
weak bisplit
weak dominating pair
weakly geodetic
weakly median
weakly modular
well covered
well-dominated
wing-triangulated
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