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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Clique cover
Definition:
Input:
A graph
G
in this class and an integer
k
.
Output:
True iff the vertices of
G
can be partitioned into
k
sets
S
i
, such that whenever two vertices are in the same set
S
i
, they are adjacent.
Linear
(0,2)-colorable ∩ chordal
1-DIR
(2,0)-colorable ∩ chordal
2-leaf power
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
,net,rising sun)-free
(2K
2
,C
4
,P
4
,triangle)-free
(2K
2
,C
4
,P
4
)-free
(2K
2
,P
3
,triangle)-free
(2K
2
,P
3
)-free
(2K
3
,2P
3
,C
4
,K
3
∪ P
3
,P
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
,P
4
)-free
(3K
1
,C
4
,C
5
)-free
(3K
1
,C
4
,
P
3
)-free
(3K
1
,P
3
)-free
(3K
1
,P
4
)-free
(3K
1
,
P
3
)-free
(3K
1
,
T
2
,
X
2
,
X
3
,anti-hole)-free
(3K
1
,paw)-free
AT-free ∩ chordal
(C
4
,P
4
,dart)-free
(C
4
,P
4
)-free
(C
4
,
P
3
,triangle)-free
(C
4
,
P
3
)-free
C
4
-free ∩ co-comparability
(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
,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+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+4
,P
5
,bull)-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
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-free
Dilworth 1
Helly circular arc
Helly circular arc ∩ (
C
7
,odd-hole)-free
Helly circular arc ∩ concave-round
Helly circular arc ∩ perfect
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
(K
2,3
,P
4
,co-butterfly)-free
K
2
-free
K
3
-minor-free
NLCT-width 1
(P
3
,triangle)-free
P
3
-free
(P
4
,co-cycle)-free
(P
4
,cycle)-free
(P
5
,bull)-free ∩ interval
(S
3
,claw,net)-free ∩ chordal
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
(XC
12
,cycle)-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
(
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
astral triple-free
binary tree
binary tree ∩ partial grid
bipartite ∩ bridged
boxicity 1
caterpillar
chordal ∩ circular arc ∩ claw-free
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ co-comparability
chordal ∩ cograph
chordal ∩ proper circular arc
chordal ∩ unit circular arc
circular arc
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ cograph
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular interval
claw-free ∩ interval
claw-free ∩ normal Helly circular arc
clique graphs of Helly circular arc
clique graphs of interval
clique graphs of normal Helly circular arc
cluster
co-biconvex
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-comparability graphs of posets of interval dimension 2, height 2
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-interval bigraph
co-interval containment bigraph
co-probe threshold
co-proper interval bigraph
co-trivially perfect ∩ trivially perfect
cograph ∩ interval
cograph ∩ split
comparability graphs of arborescence orders
comparability graphs of threshold orders
complete
complete split
concave-round
cycle-free
disjoint union of stars
hamiltonian ∩ interval
homogeneously representable
indifference
indifference ∩ split
intersection graph of nested intervals
interval
linear NLC-width 1
linear interval
lobster
maximum degree 1
normal Helly circular arc
normal circular arc
permutation ∩ split
probe complete
probe interval ∩ tree
probe threshold ∩ split
proper Helly circular arc
proper circular arc
proper interval
quasi-threshold
semicircular
split ∩ threshold signed
superfragile
threshold
tolerance ∩ tree
tree
trivially perfect
unit Helly circular arc
unit circular arc
unit interval
back to top
Polynomial
(0,2)-colorable
(0,2)-graph ∩ bipartite
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-bounded bipartite
(2,0)-colorable
(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-outerplanar
2-split ∩ perfect
2-subdivision
2-subdivision ∩ planar
2-terminal series-parallel
2-threshold
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
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
,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
,C
4
,C
5
,S
3
,co-rising sun,net)-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
)-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
,triangle)-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
)-free
(2K
2
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
(2K
2
,
C
6
,odd anti-cycle)-free
(2K
2
,odd anti-hole)-free
2K
2
-free ∩ bipartite
2K
2
-free ∩ probe cograph
2K
2
-free ∩ probe trivially perfect
(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
,2P
3
,C
n+4
,K
3
∪ P
3
)-free
(2K
3
,3K
1
,
A
,
H
,
X
45
)-free
(2K
3
,C
n+4
)-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
3
,triangle)-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
3-leaf power
3-tree
3-tree ∩ planar
(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
,butterfly,diamond)-free
(3K
1
,
2P
3
)-free
(3K
1
,
3K
2
)-free
(3K
1
,
E
)-free
(3K
1
,
H
)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
2
∪ P
4
)-free
(3K
1
,
P
6
)-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
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
,C
6
,P
7
,X
164
,X
165
,odd-cycle,sunlet
4
)-free
(3K
2
,E,P
2
∪ P
4
,net,odd anti-hole,odd-hole)-free
(3K
2
,
P
,co-gem,house)-free
(3K
2
,co-paw,odd anti-hole)-free
(3K
2
,triangle)-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
(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
,odd anti-hole,odd-hole)-free
(5,1)
(5,2)-chordal
(5,2)-crossing-chordal
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
5-leaf power
5-leaf power ∩ distance-hereditary
(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
(6,1)-chordal ∩ bipartite
(6,2)
(6,2)-chordal ∩ bipartite
(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
(7,3)
(7,4)
(8,4)
(9,6)
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,co-claw,odd anti-hole,twin-house)-free
(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,H,K
3,3
,K
3,3
-e,T
2
,X
18
,X
45
,domino,triangle)-free
(A,H,K
3,3
,X
45
,triangle)-free
(A,P
6
,clique wheel,domino,hole,house)-free
(A,T
2
,odd-cycle)-free
(A,
3P
3
,
C
n+4
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,house)-free
AC
AT-free ∩ bipartite
Apollonian network
B
0
-VPG ∩ bipartite
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
B
0
-VPG ∩ triangle-free
B
1
-CPG ∩ triangle-free
(BW
3
,C
5
,K
3,4
,K
3,4
-e,T
2
,X
18
,X
92
,X
93
,triangle)-free
BW
3
-free ∩ modular
Berge
Berge ∩ bull-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
,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
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
,P
5
)-free
(C
4
,odd-hole)-free
(C
4
,triangle)-free
(C
4
,triangle)-free ∩ planar
C
4
-free ∩ C
6
-free ∩ bipartite
C
4
-free ∩ induced-hereditary pseudo-modular
C
4
-free ∩ perfect
(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
,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
,C
6
,P
6
,triangle)-free
(C
5
,C
6
,X
164
,X
165
,sunlet
4
,triangle)-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
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-free
(C
5
,P,P
5
,S
3
,
P
,co-fork,fork,house,net)-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
2
∪ P
3
,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
,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
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
,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
,bull,co-gem,gem)-free
(C
5
,co-butterfly,co-diamond,triangle)-free
(C
5
,co-gem,gem)-free
(C
5
,co-gem,house)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
(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
,S
3
,
C
n+4
∪ K
1
,
W
4
,
W
5
,co-claw,net)-free
(C
6
,
C
6
)-free murky
(C
6
,triangle)-free
C
6
-free ∩ modular
(C
n+3
∪ K
1
,diamond,paw)-free
(C
n+4
,H)-free
(C
n+4
,K
4
)-free
(C
n+4
,P
5
,claw,gem)-free
(C
n+4
,S
3
,net)-free
(C
n+4
,S
3
)-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
,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
,odd-cycle)-free
D
Dilworth 2
Dilworth 3
Dilworth 4
(E,odd-cycle)-free
(E,triangle)-free
E-free ∩ bipartite
EPT ∩ chordal
Gallai
Gallai-perfect
(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
(H,triangle)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDG-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Halin
Helly cactus subtree ∩ perfect
Helly chordal
Helly chordal ∩ clique-chordal
Hilbertian
H
n,q
grid
(K
1,4
,odd-cycle)-free
(K
1,4
,odd-cycle)-free ∩ planar
(K
1,4
,paw)-free
(K
1,5
,triangle)-free
(K
2
∪ K
3
,P
4
,butterfly)-free
(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
,
X
163
,
X
95
,co-diamond,house)-free
(K
2
∪ claw,triangle)-free
(K
2,3
,K
4
)-minor-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
K
2,3
-free ∩ hereditary modular
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-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
,
C
n+4
)-free
(K
4
,P
4
)-free
(K
4
,S
3
,X
36
,
C
7
,
X
175
,
X
176
,
X
42
,antenna,co-claw,net,odd-hole)-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
- 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,
A
,
C
4
∪ 2K
1
,
P
2
∪ P
3
,
R
,claw,co-twin-house,odd-hole)-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
Mycielski
N
*
-perfect
(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
,co-fork,fork)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-gem,house)-free
(P
2
∪ P
4
,triangle)-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
(P
4
,
2P
3
)-free
(P
4
,triangle)-free
P
4
-brittle
P
4
-comparability
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
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
,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
,co-fork,house)-free
(P
5
,diamond)-free
(P
5
,fork,house)-free
(P
5
,gem)-free
(P
5
,triangle)-free
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
,triangle)-free
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
PI
PI
*
PURE-2-DIR
(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
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
(S
3
,
3K
2
,
E
,odd-hole)-free ∩ line
(S
3
,
C
n+4
∪ K
1
,
C(n,k)
,
W
4
,even-hole,odd-cycle ∪ K
1
)-free
(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
,net)-free ∩ chordal
(S
3
,net)-free ∩ extended P
4
-sparse
(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
V-perfect
(W
4
,claw,gem,odd-hole)-free
(W
4
,gem)-free ∩ short-chorded
Welsh-Powell opposition
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(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
172
,triangle)-free
(X
177
,odd-cycle)-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
79
,X
80
)-free ∩ modular
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
(XC
12
,triangle)-free
(XC
12
,triangle)-free ∩ planar
(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
(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
(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
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(G)-perfect
(
3K
2
,odd-hole,paw)-free
(
A
,
T
2
,odd anti-cycle)-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-paw)-free
(
K
1,4
,odd anti-cycle)-free
(
P
,butterfly,fork,gem)-free
(
P
,fork,gem)-free
(
P
,fork,house)-free
(
P
3
,triangle)-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
(
W
4
,co-claw,co-gem,odd anti-hole)-free
(
X
177
,odd anti-cycle)-free
(
X
37
,co-diamond,even anti-cycle)-free
(
XC
11
,odd anti-cycle)-free
(
XC
12
,co-cycle)-free
XC
12
-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
(
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
star
1,2,3
,odd anti-cycle)-free
τ
k
-perfect for all k >= 2
absolute bipartite retract
absolutely perfect
absorbantly perfect
almost CIS
almost median
almost tree (1)
almost-split
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,bull,odd-hole)-free
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,co-sun,hole)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
(anti-hole,odd-hole)-free
b-perfect ∩ chordal
balanced ∩ chordal
balanced ∩ co-line
balanced ∩ line
balanced ∩ paw-free
basic 4-leaf power
basic perfect
bi-cograph
biclique separable
biclique-Helly
biconvex
binary Hamming
bip
*
bipartable
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
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 ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ double split ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ split
bipartite chain
bipartite permutation
bipartite tolerance
bipolarizable
bisplit
bisplit ∩ triangle-free
bithreshold
bitolerance
block
block duplicate
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
brittle
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
cactus
charming
chordal
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ dominating pair
chordal ∩ domination perfect
chordal ∩ domino
chordal ∩ dually chordal
chordal ∩ gem-free
chordal ∩ hamiltonian
chordal ∩ hamiltonian ∩ planar
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ maximal planar
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ planar
chordal ∩ probe diamond-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal bipartite
chordal-perfect
circle graph with equator
circular convex bipartite
circular permutation
(claw ∪ 3K
1
,odd-cycle)-free
(claw,co-claw)-free
(claw,diamond,odd-hole)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd-cycle)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ mock threshold
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
clique separable
clique-perfect ∩ triangle-free
cliquewidth 2
cliquewidth 3
cliquewidth 4
co-2-subdivision
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P
4
-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-β-perfect
co-biclique separable
co-bipartite
co-bithreshold
co-bithreshold ∩ split
co-bounded tolerance
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-circular perfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
(co-claw,odd anti-hole,odd-hole)-free
co-cluster
co-comparability
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability ∪ comparability
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 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-forest-perfect
(co-fork,odd anti-cycle)-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval
co-interval ∩ cograph
co-interval ∪ interval
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-perfectly orderable
co-probe cograph
co-strongly chordal
co-threshold tolerance
co-tolerance
co-trapezoid
co-trivially perfect
co-unipolar
co-unipolar ∪ unipolar
cograph
cograph contraction
comparability
comparability ∩ distance-hereditary
comparability ∩ split
comparability ∩ weakly chordal
comparability graphs of dimension 2 posets
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 2
comparability graphs of posets of interval dimension 2, height 2
comparability graphs of posets of interval dimension 2, height 3
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
comparability graphs of series-parallel posets
complete bipartite
complete multipartite
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex
(cross,triangle)-free
cubical
cycle-bicolorable
d-trapezoid
(diamond,odd-hole)-free
diamond-free ∩ perfect
difference
directed path
distance-hereditary
domination
domination perfect ∩ triangle-free
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
double split
doubled
doubly chordal
dually chordal ∩ tripartite
even-hole-free ∩ probe chordal
extended P
4
-reducible
extended P
4
-sparse
forest-perfect
(fork,odd-cycle)-free
(fork,triangle)-free
generalized split
generalized strongly chordal
girth >=9
good
grid
grid graph
grid graph ∩ maximum degree 3
gridline
half
half-disk Helly
hamiltonian ∩ split
hereditary Helly
hereditary Matula perfect
hereditary N
*
-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary biclique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary disk-Helly
hereditary dually chordal
hereditary homogeneously orderable
hereditary median
hereditary modular
hereditary open-neighbourhood-Helly
hereditary perfect elimination bipartite
hereditary sat
(hole,odd anti-hole)-free
(hole,odd-cycle)-free
hole-free ∩ planar
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
hypercube
i-triangulated
independent module-composed
intersection graphs of parallelograms (squares)
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-outerplanar
k-path graph, fixed k
k-starlike
k-tree, fixed k
kernel solvable
leaf power
leaf power ∩ min leaf power
leaf power ∪ min leaf power
line ∩ mock threshold
line ∩ perfect
line graphs of acyclic multigraphs
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of planar cubic bipartite graphs
linear cliquewidth 2
locally perfect
matrogenic
matroidal
maxibrittle
maximal outerplanar
maximum degree 3 ∩ planar ∩ triangle-free
median
median ∩ planar
min leaf power
minimally imperfect
mock threshold
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
neighbourhood perfect
neighbourhood-Helly ∩ triangle-free
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
odd-cycle-free
(odd-hole,paw)-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable ∩ triangle-free
open-neighbourhood-Helly
opposition
outerplanar
parallelepiped
parity
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 3d grid
partial 4-tree
partial cube
partial grid
partial k-tree, fixed k
partner-limited
paw-free
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
permutation
planar ∩ triangle-free
power-chordal
premedian
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P
4
-reducible
probe P
4
-sparse
probe bipartite chain
probe bipartite distance-hereditary
probe block
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe interval bigraph
probe proper interval
probe ptolemaic
probe split
probe strongly chordal
probe threshold
probe trivially perfect
probe unit interval
proper interval bigraph
proper tolerance
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-Meyniel
quasi-brittle
quasi-parity
quasitriangulated
rectagraph
restricted block duplicate
rigid circuit
rooted directed path
semi-P
4
-sparse
semi-median
semiperfectly orderable
series-parallel
short-chorded
skeletal
slender
slightly triangulated
slim
solid grid graph
split
split ∩ strongly chordal
split ∩ superperfect
split-perfect
square of tree
star convex
strict 2-threshold
strict quasi-parity
strictly chordal
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly orderable
strongly perfect
sun-free ∩ weakly chordal
superbrittle
superperfect
thick tree
threshold signed
threshold tolerance
tolerance
tolerance ∩ triangle-free
totally unimodular
trapezoepiped
trapezoid
tree convex
tree-cograph
tree-perfect
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
triangle-free
triangulated
undirected path
unicyclic
unimodular
unipolar
unit interval bigraph
unit tolerance
very strongly perfect
weak bipolarizable
weakly chordal
wing-triangulated
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
1-string
(2,2)-interval
2-SEG
2-circular arc
2-circular track
2-interval
2-track
(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
,A,H)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,C
5
,
C
6
,net)-free
(2K
2
,C
5
)-free
(2K
2
,claw)-free
(2K
2
,co-diamond)-free
(2K
2
,net)-free
2K
2
-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
4
,house)-free
2P
3
-free
3-Helly
3-circular track
3-interval
3-mino
3-track
(3K
1
,C
5
,
C
6
,
X
164
,
X
165
,
sunlet
4
)-free
(3K
1
,
C
6
)-free
(3K
1
,
K
1,5
)-free
3K
1
-free
(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)-free
(4,0)-colorable
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
(4K
1
,co-claw,co-diamond)-free
(4K
1
,net)-free
4K
1
-free
(5,2)
5-colorable
(5-pan,T
2
,X
172
)-free
(6,1)-chordal
(6,1)-even-chordal
6-colorable
6K
1
-free
7K
1
-free
(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,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,P
6
,domino)-free
AT-free
AT-free ∩ claw-free
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
,K
4
,diamond)-free
(C
4
,C
5
,K
4
,diamond)-free ∩ planar
(C
4
,C
5
)-free
(C
4
,S
3
)-free
(C
4
,
A
,
H
)-free
(C
4
,diamond)-free
C
4
-free
(C
5
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P
5
)-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
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
3,3
+e,P,P
7
,X
37
,X
41
)-free
(C
6
,
C
6
)-free
C
6
-free
CONV
(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
,X
37
,claw,co-antenna,net,sun)-free
C
n+6
-free
C
n+7
-free
(E,P)-free
E-free
EPT
Hamiltonian hereditary
Helly
Helly 2-acyclic subtree
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
1,4
,diamond)-free
K
1,4
-free
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-free
(K
2
∪ K
3
,co-diamond)-free
K
2
∪ K
3
-free
K
2
∪ claw-free
(K
2,3
,P,P
5
)-free
(K
2,3
,P,hole)-free
(K
2,3
,P
5
)-free
(K
2,3
,X
37
,X
38
,diamond,domino,house,twin-C
5
)-free
(K
2,3
,diamond)-free
K
2,3
-free
(K
3
∪ 2K
1
,
K
3
∪ 2K
1
,bull,co-cricket,co-dart,cricket,dart)-free
(K
3,3
,K
5
)-minor-free
(K
3,3
,P
5
)-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
,S
3
)-free
K
4
-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
6
-free
K
7
-free
N
*
(P,P
5
)-free
(P,P
7
)-free
(P,P
8
)-free
(P,T
2
)-free
(P,co-fork)-free
(P,star
1,2,3
)-free
(P,star
1,2,4
)-free
(P,star
1,2,5
)-free
P-free
P
2
∪ P
4
-free
P
4
-bipartite
(P
5
,X
82
,X
83
)-free
(P
5
,
C
6
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,bull)-free
(P
5
,claw)-free
(P
5
,co-domino,co-gem)-free
(P
5
,cricket)-free
(P
5
,fork)-free
P
5
-free
(P
6
,X
30
,X
8
)-free
(P
6
,claw)-free
P
6
-free
P
7
-free
(S
3
,S
4
,net)-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
)-free
(S
3
,claw,net)-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
,claw,gem)-free
(W
4
,claw)-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
(X
91
,claw)-free
XC
10
-free
XC
13
-free
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
7
,odd-hole)-free
C
n+6
-free
C
n+7
-free
(
E
,
P
)-free
E
-free
(
K
1,4
,co-diamond)-free
(
K
1,4
,house)-free
K
1,4
-free
K
2
∪ claw
-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
,fork)-free
P
-free
P
2
∪ P
4
-free
(
P
6
,
X
30
,
X
8
)-free
P
6
-free
P
7
-free
W
2n+3
-free
(
W
4
,
W
5
,co-butterfly)-free
(
W
4
,co-claw,co-gem)-free
(
W
4
,co-claw)-free
(
W
4
,co-gem)-free
W
n+4
-free
(
X
30
,
XZ
1
,
XZ
4
,co-longhorn)-free
(
X
79
,
X
80
)-free
(
X
82
,
X
83
,house)-free
XC
10
-free
(
XC
11
,co-claw,co-diamond)-free
XC
11
-free
XC
13
-free
(n+4)-pan
-free
odd-cycle ∪ K
1
-free
all-4-simplicial
almost claw-free
alternation
anti-hole-free
apex
balanced 2-interval
biplanar
book thickness 2
boxicity 2
(bull,fork)-free
bull-free
(butterfly,claw)-free
(butterfly,gem)-free
caterpillar arboricity <= 2
circle
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular strip
circular trapezoid
(claw,diamond)-free
(claw,net)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ upper domination perfect
clique graphs
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
co-building-free
(co-butterfly,co-gem)-free
(co-claw,co-diamond)-free
co-claw-free
(co-cricket,house)-free
co-diamond-free
co-domino-free
(co-fork,house)-free
co-fork-free
co-gem-free
co-hereditary clique-Helly
co-interval filament
co-interval mixed
co-line
co-paw-free
co-planar
co-quasi-line
co-sun-free
coin
cop-win
cubic
cubic ∩ planar
diametral path
diamond-free
disk
disk contact
disk-Helly
dismantlable
dominating pair
domination perfect
domino
(domino,gem,house)-free
domino-free
dually chordal
even anti-hole-free
even-hole-free
even-signable
fork-free
gem-free
genus 0
genus 1
hereditary clique-Helly
hereditary maximal clique irreducible
hole-free
homogeneously orderable
house-free
interval filament
irredundance perfect
irredundance perfect with ir(G)<= 4
k-SEG
line
line graphs of Helly hypergraphs of rank 3
line graphs of linear hypergraphs of rank 3
line graphs of multigraphs without triangles
line graphs of triangle-free graphs
linear arboricity <= 2
linear domino
locally bipartite
locally chordal
locally connected
locally split
maximal clique irreducible
maximum degree 3
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
monopolar
(n+4)-pan-free
nK
2
-free, fixed n
nP
3
-free, fixed n
nearly bipartite
neighbourhood chordal
neighbourhood-Helly
net-free
odd anti-hole-free
odd co-sun-free
odd-cycle ∪ K
1
-free
odd-hole-free
odd-sun-free
outer-string
overlap
(p,q<=2)-colorable
partial bar visibility
partial rectangle visibility
perfect cochromatic
perfect connected-dominant
planar
planar of maximum degree 3
planar of maximum degree 4
polar
pretty
probe AT-free
probe diamond-free
pseudo-modular
quasi-line
rectangle intersection
rectangle visibility
spider graph
split-neighbourhood
strictly clique irreducible
string
strong domination perfect
subhamiltonian
subtree filament
subtree overlap
sun-free
thickness <= 2
toroidal
triangle contact
unit 2-circular arc
unit 2-circular track
unit 2-interval
unit 2-track
unit 3-circular track
unit 3-interval
unit 3-track
upper domination perfect
upper irredundance perfect
weak bar visibility
weak dominating pair
weak rectangle visibility
weakly geodetic
back to top
coNP-complete
back to top
Open
back to top
Unknown to ISGCI
(0,2)-graph
(0,3)-colorable
(1,2)-colorable
(1,2)-split
1-bounded tripartite
(2,2)-colorable
2-DIR
2-connected
2-connected ∩ (P
6
,claw)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-edge-connected
2-split
2-strongly regular
2-strongly regular ∩ planar
2-thin
(2K
2
,4K
1
,co-claw,co-diamond)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,C
5
,
T
2
)-free
(2K
2
,
2P
3
,
C
6
)-free
(2K
2
,
P
6
)-free
(2K
2
,
X
91
,co-claw)-free
(2K
2
,co-claw,co-diamond)-free
(2K
2
,house)-free
(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,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
(2K
3
+ e,
X
98
,house)-free
(2K
3
+ e,
X
99
,house)-free
(2K
3
+ e,house)-free
(2K
3
,house)-free
(2P
3
,C
4
,C
6
)-free
3-DIR
3-DIR contact
(3K
1
,C
5
,K
3
∪ K
4
,
BW
3
,
K
3,4
-e
,
T
2
,
X
18
,
X
92
,
X
93
)-free
(3K
2
,E,net,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-regular
4-regular ∩ hamiltonian
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(4K
1
,gem)-free
(4K
1
,house)-free
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular
5-regular ∩ hamiltonian
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,2)-chordal
(6,3)
(7,5)
B
0
-CPG
B
0
-VPG
B
1
-CPG
B
1
-VCPG
Birkhoff
(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
,XC
11
,claw,diamond)-free
(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
,T
2
)-free
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
(C
4
,K
4
,claw,diamond)-free
(C
4
,P
6
)-free
(C
4
,X
91
,claw)-free
(C
4
,claw,diamond)-free
(C
4
,co-claw)-free
C
4
-free ∩ odd-signable
(C
5
,P,
P
,bull,co-fork,gem,house)-free
(C
5
,P,co-fork,fork,gem,house)-free
(C
5
,P
5
,
P
,co-fork,co-gem,fork)-free
(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
,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
,house)-free
(C
7
,odd anti-hole)-free
CIS
CPG
Delaunay
Deza
E-free ∩ planar
F
n
grid
Gabriel
Hamilton-connected
Hamming
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
Helly circle
Helly subtree
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
(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
,anti-hole)-free
(K
2
∪ K
3
,
P
,house)-free
(K
2
∪ K
3
,house)-free
(K
2,3
,diamond)-free ∩ weakly modular
(K
3
∪ P
3
,
C
6
,
P
,
P
7
,
X
37
,
X
41
)-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
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
(K
4
,claw,diamond)-free
(K
4
,co-gem)-free
Laman
Laman ∩ planar
(P
2
∪ P
3
,house)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,co-fork)-free
(P
5
,house)-free
P
5
-free ∩ tripartite
P
6
-free ∩ tripartite
PURE-3-DIR
PURE-k-DIR
Raspail
(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
,
3K
2
,
E
,odd-hole)-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
Urquhart
(X
37
,diamond,even-cycle)-free
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(XC
11
,claw,diamond)-free
β-perfect
(
C
n+3
∪ K
1
,co-diamond,co-paw)-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
(
K
1,4
,
P
,co-fork,house)-free
(
P
,
P
7
)-free
(
P
,
P
8
)-free
(
P
,house)-free
(
P
6
,co-claw)-free
(
X
91
,co-claw)-free
absolute reflexive retract
(anti-hole,fork)-free
b-perfect
balanced
bar visibility
bigeodetic
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
bridged
bridged ∩ clique-Helly
building-free
building-free ∩ even-signable
building-free ∩ odd-signable
(bull,co-fork)-free
(bull,house)-free
circle ∩ diamond-free
circular perfect
(claw,odd anti-hole)-free
(claw,odd anti-hole)-free ∩ tripartite
claw-free ∩ locally connected
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ well covered
clique-Helly ∩ dismantlable ∩ reflexive
clique-perfect
(co-butterfly,co-claw)-free
(co-claw,house)-free
(co-claw,odd anti-hole)-free
(co-claw,odd-hole)-free
(co-fork,hole)-free
complete Hamming
convex-round
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
(diamond,even-cycle)-free
distance regular
distance regular of diameter 2
domination perfect ∩ planar
edge regular
equimatchable
even anti-cycle-free
even-cycle-free
extended P
4
-laden
(fork,house)-free
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
generically minimally rigid
geodetic
graceful
grid intersection
hamiltonian
hamiltonian ∩ planar
harmonious
hereditary clique-Helly ∩ self-clique
hereditary dismantlable
hereditary neighbourhood-Helly
hereditary weakly modular
homothetic triangle contact
induced-hereditary pseudo-modular
interval enumerable
interval regular
interval regular of diameter 2
irredundance perfect with ir(G)=2
isometric-HH-free
isometric-hereditary pseudo-modular
k-DIR
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
line ∩ well covered
line perfect
linear domino ∩ maximum degree 4
linearly convex triangular grid graph
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
max-tolerance
maximal planar
middle
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal
odd-signable
(p,q)-colorable
(p,q)-split
p-connected
p-tree
pairwise compatibility
partitionable
path orderable
planar ∩ strongly regular
polyhedral
probe (1,2)-colorable
probe (2,2)-colorable
probe co-bipartite
probe co-comparability
probe comparability
probe permutation
pseudo-median
(q,t)
quasi-median
reflexive
relative neighbourhood graph
self-clique
self-complementary
semi-square intersection
solid triangular grid graph
strict B
1
-VCPG
strong asteroid free
strongly even-signable
strongly odd-signable
strongly regular
triangular grid graph
tripartite
unbreakable
unigraph
unit Helly circle
unit bar visibility
unit disk
unit grid intersection
visibility
walk regular
weak bisplit
weakly median
weakly modular
well covered
well-dominated
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