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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: 3-Colourability
Definition:
Input: A graph
G
in this class.
Output: True iff each vertex of
G
can be assigned one colour out of 3 such that whenever two vertices are adjacent, they have different colours.
Linear
(0,2)-colorable
(0,2)-colorable ∩ chordal
(0,2)-graph ∩ bipartite
(0,3)-colorable
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar ∩ chordal
1-DIR
1-bounded bipartite
1-bounded tripartite
(2,0)-colorable
(2,0)-colorable ∩ chordal
(2,2)-colorable ∩ chordal
2-bounded bipartite
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-leaf power
2-outerplanar
2-subdivision
2-subdivision ∩ planar
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
,4K
1
,C
5
,co-diamond)-free
(2K
2
,4K
1
,co-claw,co-diamond)-free
(2K
2
,5K
1
,C
5
,K
3
∪ 2K
1
,P
3
∪ 2K
1
,
C
6
,
C
7
,
C
8
,
K
1,4
,
K
5
- e
,claw ∪ K
1
,co-butterfly,co-cricket,co-dart,co-gem)-free
(2K
2
,A,C
5
,
2P
3
,
X
170
,house)-free
(2K
2
,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
5
,S
3
,X
159
,X
160
,X
161
,X
162
,X
46
,X
70
,
2P
3
,
3K
2
,
H
,
P
2
∪ P
4
,
X
1
,co-rising sun,house,net)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,C
5
,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
,claw)-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,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
,C
6
,P
7
,X
164
,X
165
,odd-cycle,sunlet
4
)-free
(3K
3
,C
n+4
)-free
(3P
3
,C
n+4
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,
A
)-free
3d grid
(4,0)-colorable
(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
,co-claw,co-diamond)-free
(4K
1
,gem)-free
(4K
1
,house)-free
(4K
1
,net)-free
(4K
1
,odd anti-hole,odd-hole)-free
4K
1
-free
(5,1)
(5,2)-crossing-chordal
5-leaf power
5-leaf power ∩ distance-hereditary
5K
1
-free
(6,1)-chordal ∩ bipartite
(6,2)
(6,2)-chordal ∩ bipartite
6K
1
-free
(7,3)
(7,4)
7K
1
-free
(8,4)
(9,6)
(A,C
5
,P
5
,
A
,house,parachute,parapluie)-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,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
AT-free ∩ chordal
Apollonian network
B
0
-VPG ∩ bipartite
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
B
1
-CPG ∩ triangle-free
BW
3
-free ∩ modular
(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
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free ∩ planar
(C
4
,C
5
,C
6
,C
7
,C
8
)-free ∩ maximum degree 3 ∩ planar
(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
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
,triangle)-free ∩ planar
C
4
-free ∩ C
6
-free ∩ bipartite
C
4
-free ∩ co-comparability
C
4
-free ∩ induced-hereditary pseudo-modular
(C
5
,C
6
∪ K
1
,C
7
,K
3,3
∪ K
1
,K
3,3
-e ∪ K
1
,
K
5
- e
,domino ∪ K
1
,triangle)-free
(C
5
,C
6
,P
6
,X
17
,X
18
,X
5
,X
98
,
C
6
,
P
6
,antenna,domino)-free
(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,P
5
,house)-free
(C
5
,P
5
,
P
,house)-free
(C
5
,P
5
,co-fish,fish,house)-free
(C
5
,P
5
,house)-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
6
-free ∩ modular
(C
n+4
,H)-free
(C
n+4
,K
4
)-free
(C
n+4
,P
5
,bull)-free
(C
n+4
,P
5
,claw,gem)-free
(C
n+4
,S
3
∪ K
1
,
X
103
,claw,eiffeltower,net ∪ K
1
)-free
(C
n+4
,S
3
∪ K
1
,claw,net)-free
(C
n+4
,S
3
,claw,net)-free
(C
n+4
,S
3
,net)-free
(C
n+4
,S
3
)-free
(C
n+4
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-free
(C
n+4
,T
2
,XF
2
n+1
)-free
(C
n+4
,T
2
,net)-free
(C
n+4
,X
102
,X
204
,
P
3
∪ 2K
1
,gem)-free
(C
n+4
,X
59
,longhorn)-free
(C
n+4
,XF
1
2n+3
,XF
6
2n+2
,
X
34
,
X
36
,co-XF
2
n+1
,co-XF
3
n
)-free
(C
n+4
,
K
3
∪ 3K
1
,dart,gem)-free
(C
n+4
,bull,dart,gem)-free
(C
n+4
,claw,gem)-free
(C
n+4
,claw,net)-free
(C
n+4
,claw)-free
(C
n+4
,dart,gem)-free
(C
n+4
,diamond)-free
(C
n+4
,gem)-free
(C
n+4
,odd-sun)-free
(C
n+4
,sun)-free
C
n+4
-free
(C
n+6
,odd-cycle)-free
Dilworth 1
Dilworth 2
(E,odd-cycle)-free
(E,triangle)-free
E-free ∩ bipartite
EPT ∩ chordal
(H,triangle)-free
HHD-free ∩ co-HHD-free
HHDG-free
HHDbicycle-free
Halin
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
-free ∩ almost claw-free ∩ locally connected
(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
2,3
-free ∩ hereditary modular
K
2
-free
(K
3,3
∪ K
1
,K
4
,W
4
∪ K
1
,W
5
,X
86
,X
87
,X
88
,X
89
,X
90
,
C
7
,
X
38
,
X
39
,
butterfly ∪ K
1
,co-diamond)-free
K
3
-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
,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
,X
126
,X
174
,
3K
2
)-minor-free
Matula perfect
Meyniel ∩ co-Meyniel
NLCT-width 1
(P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(P,P
5
,
P
,co-fork,fork,house)-free
(P,
P
,co-fork,fork)-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
-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
,bull,house)-free
(P
5
,bull)-free ∩ interval
(P
5
,co-fork,house)-free
(P
5
,diamond)-free
(P
5
,fork,house)-free
(P
5
,triangle)-free
P
5
-free ∩ tripartite
(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
-free ∩ chordal bipartite
P
6
-free ∩ tripartite
(P
7
,odd-cycle,star
1,2,3
,sunlet
4
)-free
(P
7
,odd-cycle,star
1,2,3
)-free
(P
7
,odd-cycle)-free
P
7
-free ∩ bipartite
PURE-2-DIR
PURE-3-DIR
(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
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
V-perfect
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X
177
,odd-cycle)-free
(X
79
,X
80
)-free ∩ modular
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
(XC
12
,cycle)-free
(XC
12
,triangle)-free
(XC
12
,triangle)-free ∩ planar
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 ∩ 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
(
3K
2
,odd-hole,paw)-free
(
A
,
T
2
,odd anti-cycle)-free
(
C
n+3
∪ K
1
,co-diamond,co-paw)-free
(
C
n+4
,bull,house)-free
(
C
n+4
,co-claw,co-gem,house)-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
W
2n+3
-free
(
X
177
,odd anti-cycle)-free
(
XC
11
,co-claw,co-diamond)-free
(
XC
11
,odd anti-cycle)-free
XC
11
-free
(
XC
12
,co-cycle)-free
XC
12
-free
XC
13
-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
(
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
almost CIS
almost median
almost tree (1)
almost-split
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,odd anti-cycle)-free
astral triple-free
b-perfect ∩ chordal
balanced ∩ chordal
balanced ∩ paw-free
basic 4-leaf power
bi-cograph
biconvex
binary Hamming
binary tree
binary tree ∩ partial grid
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ distance-hereditary
bipartite ∩ girth>=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ grid intersection
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ module-composed
bipartite ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ unit grid intersection
bipartite ∩ weakly chordal
bipartite chain
bipartite permutation
bipartite tolerance
bisplit
bisplit ∩ triangle-free
block
block duplicate
boxicity 1
boxicity 2 ∩ co-bipartite
(bull,co-fork,fork)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(butterfly,claw)-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
chordal bipartite
circular arc ∩ co-bipartite
circular arc ∩ cograph
circular convex bipartite
(claw ∪ 3K
1
,odd-cycle)-free
(claw,co-claw)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-cycle)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ interval
claw-free ∩ locally connected
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
clique graphs of interval
clique-Helly ∩ clique-chordal
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-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
co-comparability graphs of posets of interval dimension 2, height 2
co-cycle-free
(co-diamond,diamond)-free
(co-fork,odd anti-cycle)-free
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-interval bigraph
co-interval containment bigraph
(co-paw,paw)-free
(co-paw,triangle)-free
co-planar
co-probe threshold
co-proper interval bigraph
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 posets of interval dimension 2, height 2
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete
complete bipartite
complete multipartite
complete split
convex
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cubical
cycle-free
difference
directed path
disjoint union of stars
distance-hereditary
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
doubly chordal
dually chordal
dually chordal ∩ tripartite
extended P
4
-reducible
extended P
4
-sparse
(fork,odd-cycle)-free
(fork,triangle)-free
grid
grid graph
grid graph ∩ maximum degree 3
half
half-disk Helly
hamiltonian ∩ interval
hamiltonian ∩ split
hereditary Helly
hereditary Matula perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary disk-Helly
hereditary dually chordal
hereditary median
hereditary modular
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
homogeneously representable
hypercube
independent module-composed
indifference
indifference ∩ split
intersection graph of nested intervals
interval
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-outerplanar
k-path graph, fixed k
k-tree, fixed k
leaf power
leaf power ∩ min leaf power
line graphs of acyclic multigraphs
linear NLC-width 1
linear cliquewidth 2
linear interval
linearly convex triangular grid graph
lobster
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
matrogenic
matroidal
maxibrittle
maximal outerplanar
maximal planar
maximum degree 1
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
median
median ∩ planar
minimally imperfect
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
odd anti-cycle-free
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
odd-cycle-free
(odd-hole,paw)-free
outerplanar
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 ∩ perfect
perfect ∩ triangle-free
perfect elimination bipartite
perfectly colorable
permutation ∩ split
planar ∩ triangle-free
planar of maximum degree 3
power-chordal
premedian
probe bipartite chain
probe block
probe co-trivially perfect ∩ probe trivially perfect
probe complete
probe interval ∩ tree
probe interval bigraph
probe threshold
probe threshold ∩ split
proper chordal
proper interval
proper interval bigraph
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
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
semi-median
semicircular
series-parallel
solid grid graph
solid triangular grid graph
split
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
square of tree
star convex
starlike
starlike threshold
strictly chordal
strongly 3-colorable
strongly chordal
substar
superbrittle
superfragile
thick tree
threshold
threshold signed
tolerance ∩ tree
tolerance ∩ triangle-free
tree
tree convex
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
triangular grid graph
triangulated
tripartite
trivially perfect
undirected path
unicyclic
unit interval
unit interval bigraph
weak bisplit
well-partitioned chordal
back to top
Polynomial
(1,2)-polar
2-connected ∩ (P
6
,claw)-free
2-split ∩ perfect
2-threshold
(2K
2
,A,H)-free
(2K
2
,C
4
)-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
,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,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,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
3
,triangle)-free
2P
3
-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
5
,C
7
,P
2
∪ P
4
,X
173
,
X
11
,net)-free
(3K
2
,C
5
,P
2
∪ P
4
,net)-free
(3K
2
,E,P
2
∪ P
4
,net,odd anti-hole,odd-hole)-free
(3K
2
,E,P
2
∪ P
4
,net)-free
(3K
2
,
P
,co-gem,house)-free
(3K
2
,co-paw,odd anti-hole)-free
(3K
2
,triangle)-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
(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
(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
(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,E,S
3
,X
1
,domino,hole,house,net,rising sun)-free
(A,P
6
,clique wheel,domino,hole,house)-free
(A,P
6
,domino)-free
AT-free
AT-free ∩ claw-free
Berge
Berge ∩ bull-free
Berge ∩ claw-free
(C
4
,P
5
)-free
(C
4
,P
6
)-free
(C
4
,X
91
,claw)-free
(C
4
,odd-hole)-free
C
4
-free ∩ perfect
(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
,
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
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
2
∪ P
3
)-free
(C
5
,P
5
,gem)-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
,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
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+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
,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
D
Dilworth 3
Dilworth 4
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
HH-free
HHD-free
HHDA-free
HHDS-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly cactus subtree ∩ perfect
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
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
1,4
,paw)-free
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-free
(K
2
∪ K
3
,X
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
2,3
,P,P
5
)-free
(K
2,3
,P,hole)-free
(K
2,3
,P
5
)-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
,P
5
)-free
(K
3,3
,
C
n+4
)-free
(K
3,3
-e,P
5
,X
98
)-free
(K
3,3
-e,P
5
,X
99
)-free
(K
3,3
-e,P
5
)-free
(K
4,4
,P
5
)-free
(K
4
,P
5
)-free
(K
4
,co-gem)-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
Meyniel
Meyniel ∩ weakly chordal
N
*
N
*
-perfect
(P,P
5
,
3K
2
,gem)-free
(P,P
5
,co-fork)-free
(P,P
5
)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-gem,house)-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
2
∪ P
4
,triangle)-free
P
2
∪ P
4
-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
P
4
-brittle
P
4
-comparability
P
4
-indifference
P
4
-simplicial
(P
5
,S
3
,
A
,
E
,
X
1
,anti-hole,co-domino,co-rising sun,net)-free
(P
5
,S
3
,anti-hole,co-domino,co-gem)-free
(P
5
,X
82
,X
83
)-free
(P
5
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
,gem)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,anti-hole,co-bicycle,co-domino)-free
(P
5
,anti-hole,co-domino,co-gem)-free
(P
5
,anti-hole,co-domino,co-sun)-free
(P
5
,anti-hole,co-domino)-free
(P
5
,anti-hole,co-gem)-free
(P
5
,anti-hole)-free
(P
5
,bull,co-fork)-free
(P
5
,bull,odd anti-hole)-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
,gem)-free
(P
5
,house)-free
P
5
-free
P
5
-free ∩ weakly chordal
(P
6
,X
30
,X
8
)-free
(P
6
,claw)-free
(P
6
,triangle)-free
P
6
-free
PI
PI
*
(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
(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
,claw,net)-free
(W
4
,claw,gem,odd-hole)-free
(W
4
,gem)-free ∩ short-chorded
Welsh-Powell opposition
(X
103
,
C
n+4
,
S
3
∪ K
1
,
net ∪ K
1
,co-claw,co-eiffeltower)-free
(X
12
,X
5
,X
95
,X
96
,X
97
,
X
12
,
X
5
,
X
95
,
X
96
,
X
97
,
claw ∪ triangle
,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X
172
,triangle)-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
37
,diamond,even-cycle)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
(X
91
,claw)-free
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
(XC
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
(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
β-perfect
β-perfect ∩ co-β-perfect
cal C(G)-perfect
(
C
7
,odd-hole)-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
,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
(
K
1,4
,co-diamond)-free
(
K
1,4
,co-paw)-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
absolutely perfect
absorbantly perfect
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,bull,odd-hole)-free
(anti-hole,co-sun,hole)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd-hole)-free
b-perfect
balanced ∩ co-line
balanced ∩ line
basic perfect
biclique separable
bip
*
bipartable
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
bithreshold
bitolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
brittle
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
charming
chordal ∪ co-chordal
chordal-perfect
circle graph with equator
circular arc
circular arc ∩ clique-Helly
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular interval
circular perfect
circular permutation
(claw,diamond,odd-hole)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd-hole)-free
claw-free ∩ mock threshold
claw-free ∩ normal Helly circular arc
claw-free ∩ perfect
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
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-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
(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
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-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
co-interval ∪ interval
co-leaf power
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-probe cograph
co-strongly chordal
co-tolerance
co-trapezoid
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
comparability
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 3
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
concave-round
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex-round
cycle-bicolorable
d-trapezoid
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free ∩ perfect
domination
double split
doubled
even anti-cycle-free
even-hole-free ∩ probe chordal
extended P
4
-laden
forest-perfect
generalized split
generalized strongly chordal
good
gridline
hereditary N
*
-perfect
hereditary clique-Helly ∩ line ∩ perfect
hereditary homogeneously orderable
hereditary sat
(hole,odd anti-hole)-free
hole-free
hole-free ∩ planar
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
i-triangulated
intersection graphs of parallelograms (squares)
kernel solvable
leaf power ∪ min leaf power
line ∩ mock threshold
line ∩ perfect
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of planar cubic bipartite graphs
locally perfect
min leaf power
mock threshold
module-composed
multitolerance
murky
nK
2
-free, fixed n
nP
3
-free, fixed n
neighbourhood perfect
normal Helly circular arc
normal circular arc
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-hole-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
opposition
parallelepiped
parity
path orderable
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect connected-dominant
perfectly 1-transversable
perfectly contractile
perfectly orderable
permutation
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P
4
-reducible
probe P
4
-sparse
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 proper interval
probe ptolemaic
probe split
probe strongly chordal
probe trivially perfect
probe unit interval
proper Helly circular arc
proper circular arc
proper tolerance
pseudo-split
quasi-Meyniel
quasi-brittle
quasi-parity
quasitriangulated
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
split-perfect
strict 2-threshold
strict quasi-parity
strong asteroid free
strong tree-cograph
strongly circular perfect
strongly orderable
strongly perfect
sun-free ∩ weakly chordal
superperfect
threshold tolerance
tolerance
totally unimodular
trapezoepiped
trapezoid
tree-cograph
tree-perfect
unimodular
unipolar
unit Helly circular arc
unit circular arc
unit tolerance
very strongly perfect
visibility
weak bipolarizable
weakly chordal
wing-triangulated
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
(1,2)-split
1-string
(2,2)-interval
2-DIR
2-SEG
2-circular arc
2-circular track
2-connected
2-edge-connected
2-interval
2-track
(2K
3
+ e,
X
98
,house)-free
(2K
3
+ e,
X
99
,house)-free
(2K
3
+ e,house)-free
(2K
3
,2K
3
+ e,
A
,
H
,
X
45
,
XZ
5
,co-domino)-free
(2K
3
,X
42
,
A
,
H
,
X
45
,
X
46
,
X
47
,
X
48
,
X
49
,
X
50
,
X
51
,
X
52
,
X
53
,
X
54
,
X
55
,
X
56
,
X
57
)-free
(2K
3
,house)-free
(2K
4
,house)-free
3-DIR
3-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 ∩ planar
(5,2)
5-colorable
(5-pan,T
2
,X
172
)-free
5-regular
5-regular ∩ hamiltonian
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
B
0
-CPG
B
0
-VPG
B
1
-CPG
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
)-free
(C
4
,C
5
,C
6
,S
3
)-free
(C
4
,C
5
,K
4
,diamond)-free
(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
-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
(E,P)-free
E-free
EPT
Helly 2-acyclic subtree
(K
1,4
,diamond)-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
∪ claw-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
,claw,diamond)-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
5
-free
K
6
-free
K
7
-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
4
-bipartite
(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
,
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
,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
XC
10
-free
(XC
11
,claw,diamond)-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
odd-cycle ∪ K
1
-free
all-4-simplicial
almost claw-free
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
(claw,diamond)-free
claw-free
clique graphs
clique-Helly
(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
diamond-free
disk
disk contact
domination perfect
domino
(domino,gem,house)-free
domino-free
even anti-hole-free
fork-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
house-free
k-DIR
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
linear domino ∩ maximum degree 4
locally bipartite
locally chordal
locally split
map
maximal clique irreducible
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
monopolar
(n+4)-pan-free
neighbourhood chordal
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
net-free
odd anti-hole-free
odd co-sun-free
odd-sun-free
open-neighbourhood-Helly
partial bar visibility
partial rectangle visibility
paw-free
perfect cochromatic
planar
planar of maximum degree 4
polar
pretty
probe diamond-free
quasi-line
rectangle intersection
rectangle visibility
split-neighbourhood
strictly clique irreducible
string
strong domination perfect
subhamiltonian
sun-free
thickness <= 2
toroidal
triangle contact
triangle-free
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
weak bar visibility
weak rectangle visibility
weakly geodetic
back to top
coNP-complete
back to top
Open
circle
overlap
back to top
Unknown to ISGCI
(0,2)-graph
(1,2)-colorable
(2,2)-colorable
2-split
2-strongly regular
2-strongly regular ∩ planar
2-thin
(2K
3
+ e,A,C
5
,C
6
,E,H,K
3,3
-e,R,X
168
,X
171
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,
A
,
C
6
,
E
,
H
,
R
,
X
168
,
X
171
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
3-DIR contact
3-Helly
(3K
2
,E,net,odd anti-hole)-free
4-regular ∩ hamiltonian ∩ planar
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,1)-chordal
(6,1)-even-chordal
(6,2)-chordal
(6,3)
(7,5)
B
0
-VPG ∩ triangle-free
B
1
-VCPG
(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
,XC
11
,claw,diamond)-free
(C
4
,C
5
,K
4
,diamond)-free ∩ planar
(C
4
,C
5
,T
2
)-free
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
(C
4
,K
4
,claw,diamond)-free
(C
4
,claw,diamond)-free
C
4
-free ∩ odd-signable
(C
5
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-free
(C
5
,P,co-fork,fork,gem,house)-free
(C
6
,C
8
,T
2
,X
3
,
BW
3
,
W
5
,
W
7
,
X
103
,
X
105
,
X
106
,
X
107
,
X
108
,
X
109
,
X
110
,
X
111
,
X
112
,
X
113
,
X
114
,
X
115
,
X
116
,
X
117
,
X
118
,
X
119
,
X
120
,
X
121
,
X
122
,
X
123
,
X
124
,
X
125
,
X
126
,
X
53
,
X
88
,co-X
104
)-free
(C
6
,K
3,3
+e,P,P
7
,X
37
,X
41
)-free
CIS
(C
n+3
∪ K
1
,diamond,paw)-free
C
n+6
-free
C
n+7
-free
Delaunay
Deza
E-free ∩ planar
F
n
grid
Gabriel
Hamilton-connected
Hamming
Helly
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
Helly circle
Helly subtree
K
1,4
-free ∩ well covered
(K
2,3
,diamond)-free ∩ weakly modular
K
4
-free ∩ map
K
4
-free ∩ planar
Laman
Laman ∩ planar
Mycielski
(P,P
7
)-free
(P,P
8
)-free
P
7
-free
PURE-k-DIR
Raspail
Urquhart
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(
P
,fork)-free
absolute reflexive retract
alternation
(anti-hole,fork)-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
(bull,fork)-free
circle ∩ diamond-free
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular strip
circular trapezoid
(claw,odd anti-hole)-free
claw-free ∩ upper domination perfect
claw-free ∩ well covered
clique-Helly ∩ dismantlable
clique-Helly ∩ dismantlable ∩ reflexive
clique-chordal
clique-perfect
clique-perfect ∩ triangle-free
co-circular perfect
co-interval filament
co-interval mixed
co-quasi-line
complete Hamming
cop-win
diametral path
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
domination perfect ∩ planar
edge regular
equimatchable
even-cycle-free
even-hole-free
even-signable
(fork,house)-free
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
generically minimally rigid
geodetic
graceful
harmonious
hereditary clique-Helly ∩ self-clique
hereditary dismantlable
hereditary dominating pair
hereditary weakly modular
homogeneously orderable
homothetic triangle contact
induced-hereditary pseudo-modular
interval enumerable
interval filament
interval regular
interval regular of diameter 2
irredundance perfect
irredundance perfect with ir(G)=2
irredundance perfect with ir(G)<= 4
isometric-HH-free
isometric-hereditary pseudo-modular
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
line ∩ well covered
line perfect
max-tolerance
middle
nearly bipartite
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal
odd-cycle ∪ K
1
-free
odd-signable
odd-signable ∩ triangle-free
outer-string
(p,q)-colorable
(p,q)-split
(p,q<=2)-colorable
p-connected
p-tree
pairwise compatibility
partitionable
planar ∩ strongly regular
polyhedral
probe (1,2)-colorable
probe (2,2)-colorable
probe AT-free
probe co-bipartite
probe co-comparability
probe comparability
probe permutation
pseudo-median
pseudo-modular
(q,t)
quasi-median
rectagraph
reflexive
relative neighbourhood graph
self-clique
self-complementary
semi-square intersection
spider graph
strict B
1
-VCPG
strongly even-signable
strongly odd-signable
strongly regular
subtree filament
subtree overlap
unbreakable
unigraph
unit Helly circle
unit bar visibility
unit grid intersection
universally signable
upper domination perfect
upper irredundance perfect
walk regular
weak dominating pair
weakly median
weakly modular
well covered
well-dominated
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