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