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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Independent set
Definition:
Input: A graph
G
in this class and an integer
k
.
Output: True iff
G
contains a set
S
of pairwise non-adjacent vertices, such that |
S
| >=
k
.
Linear
(0,2)-colorable ∩ chordal
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar ∩ chordal
1-DIR
1-bounded bipartite
(2,0)-colorable
(2,0)-colorable ∩ chordal
(2,2)-colorable ∩ chordal
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-leaf power
2-outerplanar
2-terminal series-parallel
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
,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
,P
3
)-free
(2K
2
,3K
1
)-free
(2K
2
,A,C
5
,
2P
3
,
X
170
,house)-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
,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
3
,triangle)-free
(2K
2
,P
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
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
(2K
2
,
C
6
,odd anti-cycle)-free
2K
2
-free ∩ bipartite
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
,2K
3
+ e,3K
1
,
A
,
H
,
T
2
,
X
18
,
X
45
,co-domino)-free
(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
,3K
1
,
A
,
H
,
X
45
)-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
(2P
3
,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
,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
,C
5
,butterfly,diamond)-free
(3K
1
,P
3
)-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
,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
(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
(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
,K
4
)-free
(4K
1
,P
4
)-free
(4K
1
,
C
n+4
)-free
(5,1)
(5,2)-crossing-chordal
5-leaf power
5-leaf power ∩ distance-hereditary
(6,2)
(6,2)-chordal ∩ bipartite
(7,3)
(7,4)
(8,4)
(9,6)
(A,E,S
3
,X
1
,domino,hole,house,net,rising sun)-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
AT-free ∩ chordal
AT-free ∩ claw-free
Apollonian network
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
(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
-free ∩ co-comparability
C
4
-free ∩ induced-hereditary pseudo-modular
(C
5
,C
6
,P
6
,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
,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
5
,gem)-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
,co-butterfly,co-diamond,triangle)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
(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
,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
,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 1
Dilworth 2
EPT ∩ chordal
(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
HHDG-free
Halin
Helly chordal
Helly chordal ∩ clique-chordal
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
1,4
-free ∩ well covered
(K
2
∪ K
3
,P
4
,butterfly)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2,3
,K
4
)-minor-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
2,3
,P
4
,co-butterfly)-free
K
2
-free
(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
3
-minor-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
-minor-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
NLCT-width 1
(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
,co-fork,fork)-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
(P
3
,triangle)-free
P
3
-free
(P
4
,
2P
3
)-free
(P
4
,co-cycle)-free
(P
4
,co-diamond,co-paw)-free
(P
4
,cycle)-free
(P
4
,diamond,paw)-free
(P
4
,triangle)-free
P
4
-extendible
P
4
-extendible ∩ P
4
-sparse
P
4
-free
P
4
-free ∩ starlike
P
4
-indifference
P
4
-laden
P
4
-lite
P
4
-reducible
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
,anti-hole,co-domino,co-gem)-free
(P
5
,
P
,gem)-free
(P
5
,bull,house)-free
(P
5
,bull,odd anti-hole)-free
(P
5
,bull)-free ∩ interval
(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 ∩ tripartite
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
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 ∩ chordal
(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
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
(X
103
,
C
n+4
,
S
3
∪ K
1
,
net ∪ K
1
,co-claw,co-eiffeltower)-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
(XC
12
,cycle)-free
(XC
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
XC
9
-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
(
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
,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
(
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
(
X
177
,odd anti-cycle)-free
(
XC
11
,odd anti-cycle)-free
(
XC
12
,co-cycle)-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
absolutely perfect
almost CIS
almost tree (1)
alternately orientable ∩ co-comparability
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,odd anti-cycle)-free
astral triple-free
b-perfect ∩ chordal
balanced ∩ chordal
basic 4-leaf power
bi-cograph
binary tree
binary tree ∩ partial grid
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ distance-hereditary
bipartite ∩ module-composed
bipartite ∩ trapezoid
bipartite chain
bipartite permutation
bipartite tolerance
block
block duplicate
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 1
boxicity 2 ∩ co-bipartite
(bull,co-fork,fork)-free
(bull,fork,gem)-free
(bull,fork,house)-free
cactus
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
circle graph with equator
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,co-claw)-free
(claw,odd-cycle)-free
(claw,paw)-free
claw-free ∩ interval
claw-free ∩ normal Helly circular arc
claw-free ∩ well covered
clique graphs of Helly circular arc
clique graphs of interval
clique graphs of normal Helly circular arc
cliquewidth 2
cluster
co-2-subdivision
co-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold ∩ split
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
(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-fork,odd anti-cycle)-free
co-interval
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-interval bigraph
co-interval containment bigraph
co-leaf power
(co-paw,odd anti-hole)-free
(co-paw,paw)-free
(co-paw,triangle)-free
co-probe threshold
co-proper interval bigraph
co-strongly chordal
co-threshold tolerance
co-trivially perfect
co-trivially perfect ∩ trivially perfect
cograph
cograph ∩ interval
cograph ∩ split
comparability ∩ distance-hereditary
comparability ∩ split
comparability graphs of arborescence orders
comparability graphs of dimension 2 posets
comparability graphs of semiorders
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete
complete bipartite
complete multipartite
complete split
concave-round
containment graph of intervals
cycle-free
d-trapezoid
difference
directed path
disjoint union of stars
distance-hereditary
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
doubly chordal
extended P
4
-laden
extended P
4
-reducible
extended P
4
-sparse
(fork,odd-cycle)-free
(fork,triangle)-free
half
hamiltonian ∩ interval
hamiltonian ∩ split
hereditary Helly
hereditary disk-Helly
hereditary dually chordal
homogeneously representable
independent module-composed
indifference
indifference ∩ split
intersection graph of nested intervals
intersection graphs of parallelograms (squares)
interval
k-outerplanar
k-path graph, fixed k
k-tree, fixed k
leaf power
leaf power ∩ min leaf power
line ∩ well covered
line graphs of acyclic multigraphs
linear NLC-width 1
linear cliquewidth 2
linear interval
lobster
matrogenic
matroidal
maximal outerplanar
maximum degree 1
min leaf power
minimally imperfect
mock threshold ∩ split
normal Helly circular arc
normal circular arc
odd anti-cycle-free
outerplanar
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 4-tree
partial k-tree, fixed k
partner-limited
permutation
permutation ∩ split
power-chordal
probe block
probe co-trivially perfect ∩ probe trivially perfect
probe complete
probe interval ∩ tree
probe proper interval
probe threshold
probe threshold ∩ split
probe unit interval
proper Helly circular arc
proper chordal
proper circular arc
proper interval
proper interval bigraph
proper tolerance
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-threshold
restricted block duplicate
rigid circuit
rooted directed path
semi-P
4
-sparse
semicircular
series-parallel
split
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
square of tree
starlike
starlike threshold
strictly chordal
strongly chordal
substar
superfragile
thick tree
threshold
threshold signed
threshold tolerance
tolerance ∩ tree
trapezoid
tree
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triangulated
trivially perfect
undirected path
unicyclic
unit Helly circular arc
unit circular arc
unit interval
unit interval bigraph
unit tolerance
well covered
well-dominated
well-partitioned chordal
back to top
Polynomial
(0,2)-colorable
(0,2)-graph ∩ bipartite
(1,2)-colorable
(1,2)-polar
1-bounded tripartite
(2,2)-colorable
2-bounded bipartite
2-connected ∩ (P
6
,claw)-free
2-split
2-split ∩ perfect
2-thin
2-threshold
(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,H)-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
,
2P
3
,
C
6
)-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
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
,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
(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
,C
4
,C
6
)-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
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
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
,E,P
2
∪ P
4
,net)-free
(3K
2
,
P
,co-gem,house)-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
3d grid
(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
,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
(5,2)-chordal
(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
5K
1
-free
(6,1)-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
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,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,P
6
,clique wheel,domino,hole,house)-free
(A,P
6
,domino)-free
(A,T
2
,odd-cycle)-free
AT-free
B
0
-VPG ∩ bipartite
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
,XC
11
,claw,diamond)-free
(C
4
,C
5
,T
2
)-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
5
)-free
(C
4
,P
6
)-free
(C
4
,X
91
,claw)-free
(C
4
,claw,diamond)-free
(C
4
,odd-hole)-free
C
4
-free ∩ C
6
-free ∩ bipartite
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
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P,P
5
,house)-free
(C
5
,P,co-fork,fork,gem,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
,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
,house)-free
(C
5
,P
5
)-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
,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
,K
3,3
+e,P,P
7
,X
37
,X
41
)-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
,S
3
,
C
n+4
∪ K
1
,
W
4
,
W
5
,co-claw,net)-free
(C
6
,
C
6
)-free murky
C
6
-free ∩ modular
(C
n+3
∪ K
1
,diamond,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
,XF
2
n+1
,XF
3
n
,XF
4
n
)-free
(C
n+6
,odd-cycle)-free
D
Dilworth 3
Dilworth 4
(E,P)-free
(E,odd-cycle)-free
E-free ∩ bipartite
E-free ∩ planar
EPT
F
n
grid
Gallai
Gallai-perfect
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly cactus subtree ∩ perfect
Helly circle
Hilbertian
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
1,4
,odd-cycle)-free
(K
1,4
,odd-cycle)-free ∩ planar
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-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
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2
∪ K
3
,co-diamond)-free
(K
2
∪ claw,triangle)-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
-free ∩ hereditary modular
(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
,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
,P
5
)-free
(K
4
,S
3
,X
36
,
C
7
,
X
175
,
X
176
,
X
42
,antenna,co-claw,net,odd-hole)-free
(K
4
,claw,diamond)-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
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
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N
*
N
*
-perfect
(P,P
5
,co-fork)-free
(P,P
5
)-free
(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-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
,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
2
∪ P
3
,house)-free
P
4
-brittle
P
4
-comparability
P
4
-simplicial
(P
5
,S
3
,
A
,
E
,
X
1
,anti-hole,co-domino,co-rising sun,net)-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
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)-free
(P
5
,claw)-free
(P
5
,co-domino,co-gem)-free
(P
5
,co-fork)-free
(P
5
,cricket)-free
(P
5
,fork)-free
(P
5
,house)-free
P
5
-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
,X
30
,X
8
)-free
(P
6
,claw)-free
(P
6
,triangle)-free
P
6
-free
P
6
-free ∩ tripartite
(P
7
,odd-cycle)-free
P
7
-free ∩ bipartite
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
,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
,
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
,claw,net)-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
,claw,gem)-free
(W
4
,claw)-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
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
79
,X
80
)-free ∩ modular
(X
91
,claw)-free
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
(XC
11
,claw,diamond)-free
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
(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
cal C(G)-perfect
(
3K
2
,odd-hole,paw)-free
(
K
1,4
,co-diamond)-free
(
K
1,4
,co-paw)-free
(
P
,fork)-free
W
2n+3
-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
(
X
37
,co-diamond,even anti-cycle)-free
XC
10
-free
(
XC
11
,co-claw,co-diamond)-free
XC
11
-free
XC
12
-free
XC
13
-free
odd-cycle ∪ K
1
-free
absolute bipartite retract
absorbantly perfect
almost median
almost-split
alternately colourable
alternately orientable
(anti-hole,bull,odd-hole)-free
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd-hole)-free
b-perfect
balanced ∩ co-line
balanced ∩ line
balanced ∩ paw-free
basic perfect
biclique separable
biconvex
binary Hamming
bip
*
bipartable
bipartite
bipartite ∩ boxicity 2
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
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 ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
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
bipolarizable
bisplit
bisplit ∩ triangle-free
bithreshold
bitolerance
brittle
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
(bull,fork)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
(butterfly,claw)-free
charming
chordal ∪ co-chordal
chordal bipartite
chordal-perfect
circle
circle ∩ diamond-free
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular convex bipartite
circular permutation
circular strip
circular trapezoid
(claw ∪ 3K
1
,odd-cycle)-free
(claw,diamond,odd-hole)-free
(claw,diamond)-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-free
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
claw-free ∩ upper domination perfect
clique separable
cliquewidth 3
cliquewidth 4
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-bithreshold
co-bounded tolerance
co-building-free
(co-butterfly,co-gem)-free
co-circular perfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,odd anti-hole,odd-hole)-free
(co-claw,odd-hole)-free
co-comparability ∪ comparability
(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-gem,gem)-free
(co-gem,house)-free
co-gem-free
co-hereditary clique-Helly
co-interval ∪ interval
co-interval filament
co-interval mixed
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-planar
co-probe cograph
co-quasi-line
co-tolerance
co-trapezoid
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
comparability
comparability ∩ weakly chordal
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
containment graph of circles
containment graphs
containment graphs of circular arcs
convex
convex-round
cubical
cycle-bicolorable
(diamond,odd-hole)-free
diamond-free ∩ perfect
domination
domino
double split
doubled
dually chordal ∩ tripartite
even anti-cycle-free
even-hole-free ∩ probe chordal
forest-perfect
(fork,house)-free
fork-free
fuzzy circular interval
fuzzy linear interval
generalized split
generalized strongly chordal
good
grid
grid graph
grid graph ∩ maximum degree 3
gridline
half-disk 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 clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary homogeneously orderable
hereditary median
hereditary modular
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
interval bigraph
interval containment bigraph
interval filament
isometric subgraph of a hypercube
k-polygon
kernel solvable
leaf power ∪ min leaf power
line
line ∩ mock threshold
line ∩ perfect
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of multigraphs without triangles
line graphs of planar cubic bipartite graphs
line graphs of triangle-free graphs
linear domino
linear domino ∩ maximum degree 4
locally perfect
maxibrittle
median
median ∩ planar
middle
mock threshold
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
(n+4)-pan-free
nK
2
-free, fixed n
nearly bipartite
neighbourhood perfect
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-cycle ∪ K
1
-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
opposition
overlap
(p,q<=2)-colorable
parallelepiped
parity
partial 3d grid
partial cube
partial grid
path orderable
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect connected-dominant
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
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 chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe interval bigraph
probe ptolemaic
probe split
probe strongly chordal
probe trivially perfect
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
quasi-Meyniel
quasi-brittle
quasi-line
quasi-parity
quasitriangulated
semi-median
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
solid grid graph
spider graph
split-perfect
star convex
strict 2-threshold
strict quasi-parity
strong asteroid free
strong tree-cograph
strongly 3-colorable
strongly circular perfect
strongly orderable
strongly perfect
subtree filament
subtree overlap
sun-free ∩ weakly chordal
superbrittle
superperfect
tolerance
tolerance ∩ triangle-free
totally unimodular
trapezoepiped
tree convex
tree-cograph
tree-perfect
triad convex
unimodular
unipolar
unit Helly circle
very strongly perfect
weak bipolarizable
weakly chordal
wing-triangulated
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
(0,3)-colorable
(1,2)-split
1-string
(2,2)-interval
2-DIR
2-SEG
2-circular arc
2-circular track
2-connected
2-connected ∩ cubic ∩ planar
2-edge-connected
2-interval
2-subdivision
2-subdivision ∩ planar
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-Helly
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
4-regular
4-regular ∩ hamiltonian
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(5,2)
5-colorable
5-regular
5-regular ∩ hamiltonian
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
6-colorable
(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
B
0
-CPG
B
0
-VPG
B
0
-VPG ∩ triangle-free
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
,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
,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
)-free
(C
4
,C
5
,C
6
,S
3
)-free
(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
,co-claw)-free
(C
4
,diamond)-free
(C
4
,triangle)-free
(C
4
,triangle)-free ∩ planar
C
4
-free
(C
5
,C
6
,X
164
,X
165
,sunlet
4
,triangle)-free
(C
5
,P,
P
,bull,co-fork,gem,house)-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
,triangle)-free
C
6
-free
(C
7
,odd anti-hole)-free
CONV
CPG
(H,triangle)-free
Helly
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
,anti-hole)-free
(K
2
∪ K
3
,
P
,house)-free
(K
2
∪ K
3
,house)-free
K
2
∪ K
3
-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
∪ 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,co-fork)-free
P-free
P
4
-bipartite
PURE-3-DIR
PURE-k-DIR
(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
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
all-4-simplicial
alternation
anti-hole-free
apex
balanced 2-interval
biclique-Helly
biplanar
book thickness 2
boxicity 2
building-free
(bull,co-fork)-free
(bull,house)-free
bull-free
(butterfly,gem)-free
caterpillar arboricity <= 2
clique graphs
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
(co-butterfly,co-claw)-free
(co-claw,house)-free
(co-claw,odd anti-hole)-free
co-claw-free
(co-cricket,house)-free
co-domino-free
(co-fork,house)-free
co-fork-free
co-sun-free
coin
cop-win
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
diamond-free
disk
disk contact
disk-Helly
dismantlable
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
(domino,gem,house)-free
domino-free
dually chordal
even anti-hole-free
gem-free
genus 0
genus 1
girth>=9
grid intersection
hamiltonian
hamiltonian ∩ planar
hereditary biclique-Helly
hereditary clique-Helly
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
homogeneously orderable
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 connected
locally split
map
maximal clique irreducible
maximum degree 3
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
monopolar
neighbourhood chordal
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
net-free
odd anti-hole-free
odd co-sun-free
odd-sun-free
open-neighbourhood-Helly
p-connected
partial bar visibility
partial rectangle visibility
paw-free
perfect cochromatic
planar
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polar
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe diamond-free
pseudo-modular
rectangle intersection
rectangle visibility
split-neighbourhood
strictly clique irreducible
string
strong domination perfect
subhamiltonian
sun-free
thickness <= 2
toroidal
triangle contact
triangle-free
tripartite
unit 2-circular arc
unit 2-circular track
unit 2-interval
unit 2-track
unit 3-circular track
unit 3-interval
unit 3-track
unit disk
visibility
weak bar visibility
weak bisplit
weak rectangle visibility
weakly geodetic
back to top
coNP-complete
back to top
Open
2P
3
-free
back to top
Unknown to ISGCI
(0,2)-graph
2-connected ∩ linearly convex triangular grid graph
2-strongly regular
2-strongly regular ∩ planar
(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
,triangle)-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,net,odd anti-hole)-free
(3K
2
,triangle)-free
(5-pan,T
2
,X
172
)-free
(5-pan,T
2
,X
172
)-free ∩ planar
(6,1)-chordal
(6,1)-even-chordal
(6,2)-chordal
(6,3)
(7,5)
(A,H,K
3,3
,K
3,3
-e,T
2
,X
18
,X
45
,domino,triangle)-free
(BW
3
,C
5
,K
3,4
,K
3,4
-e,T
2
,X
18
,X
92
,X
93
,triangle)-free
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 ∩ planar
(C
4
,C
5
,C
6
,C
7
,C
8
)-free ∩ maximum degree 3 ∩ planar
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
C
4
-free ∩ odd-signable
(C
5
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-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
CIS
C
n+6
-free
C
n+7
-free
Delaunay
Deza
(E,triangle)-free
E-free
Gabriel
Hamilton-connected
Hamming
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
Helly subtree
H
n,q
grid
K
1,4
-free ∩ almost claw-free ∩ locally connected
(K
2,3
,diamond)-free ∩ weakly modular
Laman
Laman ∩ planar
Mycielski
(P
2
∪ P
4
,triangle)-free
P
2
∪ P
4
-free
P
7
-free
Raspail
(S
3
,T
2
,X
205
,X
206
,X
207
,X
208
,
X
42
)-free
(S
3
,
3K
2
,
E
,odd-hole)-free
Urquhart
(X
37
,diamond,even-cycle)-free
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(XC
12
,triangle)-free ∩ planar
β-perfect
(
C
7
,odd-hole)-free
absolute reflexive retract
almost claw-free
balanced
bar visibility
bigeodetic
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
bridged
bridged ∩ clique-Helly
building-free ∩ even-signable
building-free ∩ odd-signable
circular perfect
clique-Helly ∩ dismantlable ∩ reflexive
clique-perfect
clique-perfect ∩ triangle-free
complete Hamming
diametral path
(diamond,even-cycle)-free
distance regular
distance regular of diameter 2
edge regular
equimatchable
even-cycle-free
even-hole-free
even-signable
frame hereditary dominating pair
fully cycle extendable
generically minimally rigid
geodetic
graceful
harmonious
hereditary clique-Helly ∩ self-clique
hereditary dismantlable
hereditary dominating pair
hereditary weakly modular
hole-free
homothetic triangle contact
induced-hereditary pseudo-modular
interval enumerable
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-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
line perfect
linearly convex triangular grid graph
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
max-tolerance
maximal planar
maximum degree 3 ∩ planar ∩ triangle-free
nP
3
-free, fixed n
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal
odd-hole-free
odd-signable
odd-signable ∩ triangle-free
outer-string
(p,q)-colorable
(p,q)-split
p-tree
pairwise compatibility
partitionable
planar ∩ strongly regular
polyhedral
probe AT-free
probe co-bipartite
probe co-comparability
probe comparability
probe permutation
pseudo-median
(q,t)
quasi-median
rectagraph
reflexive
relative neighbourhood graph
self-clique
self-complementary
semi-square intersection
solid triangular grid graph
strict B
1
-VCPG
strongly even-signable
strongly odd-signable
strongly regular
triangular grid graph
unbreakable
unigraph
unit bar visibility
unit grid intersection
universally signable
upper domination perfect
upper irredundance perfect
walk regular
weak dominating pair
weakly median
weakly modular
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