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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Graph canonisation
Definition:
Input:
A graph
G
in this class.
Output:
A graph
C(G)
such that
C(G) = C(H)
iff
G
is isomorphic to
H
.
Linear
(0,2)-colorable ∩ chordal
(2K
2
,C
4
,P
4
,triangle)-free
(2K
2
,P
3
,triangle)-free
(C
4
,
P
3
,triangle)-free
K
2
-free
K
3
-minor-free
(P
3
,triangle)-free
(P
4
,cycle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
(XC
12
,cycle)-free
binary tree
binary tree ∩ partial grid
bipartite ∩ bridged
caterpillar
cycle-free
disjoint union of stars
linear forest
lobster
maximum degree 1
probe interval ∩ tree
tolerance ∩ tree
tree
back to top
Polynomial
(0,3)-colorable ∩ chordal
1-DIR
1-bounded bipartite
(2,0)-colorable ∩ chordal
2-bounded bipartite
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
,A,C
5
,S
3
,X
159
,X
219
,
C
6
,
E
,
P
6
,
X
159
,
X
219
,
X
58
,co-rising sun,net,rising sun)-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
,claw,diamond)-free
(2K
2
,C
4
,C
5
,co-claw,co-diamond)-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
)-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 cograph
2K
2
-free ∩ probe trivially perfect
(2K
3
+ e,A,C
5
,C
6
,E,H,K
3,3
-e,P
6
,R,S
3
,X
166
,X
167
,X
168
,X
169
,X
170
,X
171
,X
172
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,X
96
,X
98
,
A
,
C
6
,
E
,
H
,
P
6
,
R
,
X
166
,
X
167
,
X
168
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
96
,
X
98
,antenna,co-antenna,co-cross,co-domino,co-fish,co-twin-house,cross,domino,fish,net,twin-house)-free
(2K
3
,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
,C
5
,K
5
- e,
C
6
∪ K
1
,
C
7
,
K
3,3
∪ K
1
,
K
3,3
-e ∪ K
1
,
domino ∪ K
1
)-free
(3K
1
,C
5
,
C
6
,
P
6
)-free
(3K
1
,C
5
,butterfly,diamond)-free
(3K
1
,P
3
)-free
(3K
1
,P
4
)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
3
)-free
(3K
1
,
P
6
)-free
(3K
1
,
X
172
)-free
(3K
1
,co-fork)-free
(3K
1
,house)-free
(3K
1
,paw)-free
(3K
2
,C
4
∪ P
2
,C
5
,P
2
∪ P
4
,P
5
,S
3
,X
1
,X
46
,X
70
,
3K
2
,
C
4
∪ P
2
,
P
2
∪ P
4
,
X
1
,
X
46
,
X
70
,co-fish,co-rising sun,fish,house,net,rising sun)-free
(3K
2
,C
5
,P
2
∪ P
4
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
,net)-free
(3K
2
,C
6
,P
7
,X
164
,X
165
,odd-cycle,sunlet
4
)-free
(3K
2
,
P
,co-gem,house)-free
4-leaf power
(4K
1
,K
4
)-free
(4K
1
,P
4
)-free
(4K
1
,
C
n+4
)-free
(5,1)
(5,2)-crossing-chordal
5-leaf power
5-leaf power ∩ distance-hereditary
(6,2)
(6,2)-chordal ∩ bipartite
(7,3)
(7,4)
(8,4)
(9,6)
(A,T
2
,odd-cycle)-free
AC
AT-free ∩ chordal
Apollonian network
(C
4
,C
5
,C
6
,E,P
6
,S
3
,X
159
,X
219
,X
58
,
A
,
X
159
,
X
219
,co-rising sun,net,rising sun)-free
(C
4
,P
4
,dart)-free
(C
4
,P
4
,diamond,paw)-free
(C
4
,P
4
)-free
(C
4
,
P
3
)-free
C
4
-free ∩ co-comparability
C
4
-free ∩ galled-tree explainable
(C
5
,C
6
∪ K
1
,C
7
,K
3,3
∪ K
1
,K
3,3
-e ∪ K
1
,
K
5
- e
,domino ∪ K
1
,triangle)-free
(C
5
,C
6
,P
6
,triangle)-free
(C
5
,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
5
,gem)-free
(C
5
,S
3
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
3K
2
,
P
2
∪ P
4
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free ∩ P
4
-tidy
(C
5
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,bull,co-gem,gem)-free
(C
5
,co-butterfly,co-diamond,triangle)-free
(C
5
,co-gem,gem)-free
(C
5
,co-gem,house)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
(C
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
,claw,net)-free
(C
n+4
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-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
Dilworth 1
Dilworth 2
(E,odd-cycle)-free
E-free ∩ bipartite
HHDG-free
Halin
(K
2
∪ K
3
,P
4
,butterfly)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2
∪ claw,triangle)-free
(K
2,3
,K
4
)-minor-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
2,3
,P
4
,co-butterfly)-free
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-free
(K
4
,P
4
)-free
K
4
-minor-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
NLCT-width 1
(P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(P,P
5
,
3K
2
,gem)-free
(P,P
5
,
P
,co-fork,fork,house)-free
(P,P
5
,co-fork)-free
(P,
P
,co-fork,fork)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-gem,house)-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
P
3
-free
(P
4
,
2P
3
)-free
(P
4
,co-cycle)-free
(P
4
,co-diamond,co-paw,diamond,paw)-free
(P
4
,co-diamond,co-paw)-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
-lite
P
4
-reducible
P
4
-sparse
P
4
-tidy
P
4
-tidy ∩ (S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
P
4
-tidy ∩ balanced
P
4
-tidy ∩ hereditary clique-Helly ∩ perfect
P
4
-tidy ∩ perfect
(P
5
,S
3
,anti-hole,co-domino,co-gem)-free
(P
5
,
P
,gem)-free
(P
5
,anti-hole,co-domino,co-gem)-free
(P
5
,bull,co-fork)-free
(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
,gem)-free
(P
5
,triangle)-free
(P
6
,triangle)-free
P
6
-free ∩ chordal bipartite
(P
7
,odd-cycle,star
1,2,3
,sunlet
4
)-free
(P
7
,odd-cycle,star
1,2,3
)-free
(S
3
,
C
n+4
,co-claw,net)-free
(S
3
,claw,net)-free ∩ chordal
(S
3
,net)-free ∩ extended P
4
-sparse
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(X
172
,triangle)-free
(X
177
,odd-cycle)-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
(
2C
4
,
3K
2
,
C
6
,
E
,
P
2
∪ P
4
,
P
6
,
X
25
,
X
26
,
X
27
,
X
28
,
X
29
,odd anti-cycle)-free
(
3K
2
,
C
6
,
P
7
,
X
164
,
X
165
,
sunlet
4
,odd anti-cycle)-free
(
A
,
T
2
,odd anti-cycle)-free
(
C
n+4
,
T
2
,
X
31
,co-XF
2
n+1
,co-XF
3
n
)-free
(
C
n+4
,bull,co-dart,co-gem)-free
(
C
n+4
,bull,house)-free
(
C
n+4
,co-claw,co-gem,house)-free
(
C
n+4
,co-claw,co-gem)-free
(
C
n+4
,co-dart,co-gem)-free
(
C
n+4
,co-diamond)-free
(
C
n+4
,co-gem)-free
(
E
,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
(
T
2
,co-cycle)-free
(
T
3
,
X
81
,co-cycle)-free
(
T
3
,co-cycle)-free
(
X
177
,odd anti-cycle)-free
(
XC
12
,co-cycle)-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
(
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
star
1,2,3
,odd anti-cycle)-free
almost tree (1)
(anti-hole,co-domino,odd anti-cycle)-free
astral triple-free
bi-cograph
bipartite ∩ bithreshold
bipartite ∩ claw-free
bipartite ∩ distance-hereditary
bipartite ∩ module-composed
bipartite chain
block
block duplicate
boxicity 1
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
cactus
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ co-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
chordal ∩ unit circular arc
circular arc ∩ cograph
(claw ∪ 3K
1
,odd-cycle)-free
(claw,co-claw)-free
(claw,odd-cycle)-free
(claw,paw)-free
claw-free ∩ interval
clique graphs of interval
cliquewidth 2
cliquewidth 3
cliquewidth 4
cluster
co-bithreshold ∩ split
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-cycle)-free
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,house)-free
(co-fork,odd anti-cycle)-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-interval ∪ interval
(co-paw,paw)-free
(co-paw,triangle)-free
co-probe cograph
co-probe threshold
co-trivially perfect
co-trivially perfect ∩ trivially perfect
co-unit interval
cograph
cograph ∩ interval
cograph ∩ split
comparability ∩ distance-hereditary
comparability ∩ split
comparability graphs of arborescence orders
comparability graphs of semiorders
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete
complete bipartite
complete multipartite
complete split
difference
distance-hereditary
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
extended P
4
-reducible
extended P
4
-sparse
(fork,odd-cycle)-free
(fork,triangle)-free
half
hamiltonian ∩ interval
homogeneously representable
independent module-composed
indifference
indifference ∩ split
intersection graph of nested intervals
interval
k-outerplanar
k-path graph, fixed k
k-tree, fixed k
line graphs of acyclic multigraphs
linear NLC-width 1
linear cliquewidth 2
linear interval
matrogenic
matroidal
maximal outerplanar
minimally imperfect
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
outerplanar
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 4-tree
partial k-tree, fixed k
partner-limited
permutation ∩ split
probe P
4
-reducible
probe P
4
-sparse
probe bipartite chain
probe bipartite distance-hereditary
probe block
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe complete
probe distance-hereditary
probe ptolemaic
probe threshold
probe threshold ∩ split
probe trivially perfect
proper interval
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-threshold
restricted block duplicate
semi-P
4
-sparse
semicircular
series-parallel
split ∩ superperfect
split ∩ threshold signed
starlike threshold
strictly chordal
strong tree-cograph
superfragile
thick tree
threshold
threshold signed
tree-cograph
treewidth 2
treewidth 3
treewidth 4
treewidth 5
trivially perfect
unicyclic
unit interval
back to top
GI-complete
(0,2)-colorable
(0,3)-colorable
(1,1)-colorable
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
(1,2)-split
(2,0)-colorable
(2,1)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
(2,2)-interval
2-SEG
2-circular arc
2-circular track
2-interval
2-split
2-split ∩ perfect
2-subdivision
2-track
(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
,A,C
5
,
2P
3
,
X
170
,house)-free
(2K
2
,A,H)-free
(2K
2
,C
4
,C
5
)-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
,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,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,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,
X
98
,house)-free
(2K
3
+ e,
X
99
,house)-free
(2K
3
+ e,house)-free
(2K
3
,2K
3
+ e,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,W
4
,X
84
,X
95
,
A
,
C
6
,
P
6
,
X
5
,
X
98
,butterfly,co-domino,co-fish,fish)-free
(2K
3
,2K
3
+ e,
A
,
H
,
X
45
,
XZ
5
,co-domino)-free
(2K
3
,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,X
84
,
3K
2
,
C
4
∪ P
2
,
C
6
,
P
2
∪ P
4
,
P
6
,
X
18
,
X
5
,co-antenna,co-domino,co-fish)-free
(2K
3
,2P
3
,C
n+4
,K
3
∪ P
3
)-free
(2K
3
,3K
1
,
A
,
H
,
X
45
)-free
(2K
3
,C
n+4
)-free
(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
,C
4
,C
5
,P
5
,X
170
,
A
)-free
(2P
3
,C
4
,C
6
)-free
2P
3
-free
3-Helly
3-circular track
3-interval
3-mino
3-track
(3K
1
,C
5
,
C
6
,
X
164
,
X
165
,
sunlet
4
)-free
(3K
1
,
C
6
)-free
(3K
1
,
H
)-free
3K
1
-free
(3K
2
,A,C
4
∪ 2K
1
,E,P
2
∪ P
3
,R,
K
5
- e
,co-claw,net,odd anti-hole,twin-house)-free
(3K
2
,C
4
∪ P
2
,C
5
,C
6
,K
2
∪ K
3
,K
3,3
,K
3,3
+e,P
2
∪ P
4
,P
6
,X
18
,X
5
,
2P
3
,
C
6
,
C
7
,
X
84
,antenna,domino,fish)-free
(3K
2
,C
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
(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
(3P
3
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,X
184
,X
185
,X
186
,X
187
,X
188
,X
189
,X
190
,X
191
,X
192
,X
193
,
5-pan
,
A
,
P
6
,co-twin-C
5
)-free
(4,0)-colorable
4-colorable
(4-fan,K
1,4
,W
4
,W
5
,
A ∪ K
1
,
co-fork ∪ K
1
,
gem ∪ K
1
,
net ∪ K
1
)-free
(4K
1
,C
7
,S
3
,X
175
,X
176
,X
42
,
X
36
,claw,co-antenna,net,odd anti-hole)-free
(4K
1
,gem)-free
(4K
1
,net)-free
(4K
1
,odd anti-hole,odd-hole)-free
4K
1
-free
(5,2)
(5,2)-chordal
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
5-colorable
(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
5K
1
-free
(6,1)-chordal
(6,1)-chordal ∩ bipartite
(6,1)-even-chordal
(6,2)-chordal
6-colorable
(6-fan,C
4
∪ P
2
,C
5
,C
6
∪ K
1
,C
7
,K
2
∪ K
3
,K
2,3
,P
2
∪ P
4
,W
4
∪ K
1
,W
6
,X
132
,X
169
,X
176
,X
18
,X
197
,X
198
,X
199
,X
200
,X
201
,X
202
,X
35
,X
84
,
C
4
∪ P
2
,
C
6
∪ K
1
,
C
7
,
P
2
∪ P
4
,
W
4
∪ K
1
,
W
6
,
X
132
,
X
169
,
X
176
,
X
18
,
X
197
,
X
198
,
X
199
,
X
200
,
X
201
,
X
35
,
X
84
,
butterfly ∪ K
1
,butterfly ∪ K
1
,co-6-fan,co-fish,fish)-free
6K
1
-free
7K
1
-free
(A ∪ K
1
,
K
1,4
,
W
4
,
W
5
,co-4-fan,co-fork ∪ K
1
,gem ∪ K
1
,net ∪ K
1
)-free
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,
W
5
,co-claw,twin-C
5
,twin-house)-free
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,co-claw,odd anti-hole,twin-house)-free
(A,C
5
,C
6
,K
2
∪ K
3
,K
3,3
,K
3,3
+e,K
3,3
-e,P
6
,X
5
,X
98
,
2P
3
,
C
6
,
C
7
,
W
4
,
X
84
,
X
95
,co-butterfly,co-fish,domino,fish)-free
(A,C
5
,C
6
,P
6
,domino,house)-free
(A,C
5
,P
5
,
A
,house,parachute,parapluie)-free
(A,H,K
3,3
,K
3,3
-e,X
45
,XZ
5
,domino)-free
(A,H,K
3,3
,X
45
,X
46
,X
47
,X
48
,X
49
,X
50
,X
51
,X
52
,X
53
,X
54
,X
55
,X
56
,X
57
,
X
42
)-free
(A,H,K
3,3
,X
45
,triangle)-free
(A,P
6
,domino)-free
(A,
3P
3
,
C
n+4
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,house)-free
AT-free
AT-free ∩ claw-free
B
1
-VPG
B
2
-VPG
B
3
-VPG
(BW
3
,W
5
,W
7
,X
103
,X
104
,X
105
,X
106
,X
107
,X
108
,X
109
,X
110
,X
111
,X
112
,X
113
,X
114
,X
115
,X
116
,X
117
,X
118
,X
119
,X
120
,X
121
,X
122
,X
123
,X
124
,X
125
,X
126
,X
53
,X
88
,
C
6
,
C
8
,
T
2
,
X
3
)-free
BW
3
-free
BW
3
-free ∩ modular
Berge
Berge ∩ bull-free
Berge ∩ claw-free
B
k
-VPG
Bouchet
(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,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
)-free
(C
4
,C
5
,C
6
,S
3
)-free
(C
4
,C
5
,K
4
,diamond)-free
(C
4
,C
5
,T
2
)-free
(C
4
,C
5
)-free
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
(C
4
,P
5
)-free
(C
4
,P
6
)-free
(C
4
,S
3
)-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
-free
C
4
-free ∩ induced-hereditary pseudo-modular
C
4
-free ∩ odd-signable
C
4
-free ∩ perfect
C
4
-free ∩ weakly modular
(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
,X
164
,X
165
,sunlet
4
,triangle)-free
(C
5
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P,P
5
,
P
,house)-free
(C
5
,P,P
5
,house)-free
(C
5
,P,
P
,bull,co-fork,gem,house)-free
(C
5
,P
2
∪ P
3
,house)-free
(C
5
,P
5
,
A
,
C
6
,
P
6
,co-domino)-free
(C
5
,P
5
,
P
,house)-free
(C
5
,P
5
,
P
2
∪ P
3
)-free
(C
5
,P
5
,co-fish,fish,house)-free
(C
5
,P
5
,house)-free
(C
5
,P
5
)-free
(C
5
,P
6
,
P
6
)-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free
(C
5
,house)-free
C
5
-free
(C
6
,C
8
,T
2
,X
3
,
BW
3
,
W
5
,
W
7
,
X
103
,
X
105
,
X
106
,
X
107
,
X
108
,
X
109
,
X
110
,
X
111
,
X
112
,
X
113
,
X
114
,
X
115
,
X
116
,
X
117
,
X
118
,
X
119
,
X
120
,
X
121
,
X
122
,
X
123
,
X
124
,
X
125
,
X
126
,
X
53
,
X
88
,co-X
104
)-free
(C
6
,K
3,3
+e,P,P
7
,X
37
,X
41
)-free
(C
6
,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
(C
6
,
C
6
)-free murky
(C
6
,house)-free
(C
6
,triangle)-free
C
6
-free
C
6
-free ∩ modular
(C
7
,odd anti-hole)-free
CONV
(C
n+4
,S
3
)-free
(C
n+4
,X
59
,longhorn)-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
,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
,X
37
,claw,co-antenna,net,sun)-free
(C
n+6
,odd-cycle)-free
C
n+6
-free
C
n+7
-free
(E,P)-free
E-free
EPT
Gallai
Gallai-perfect
(H,triangle)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly
Helly 2-acyclic subtree
Helly ∩ bridged
Helly chordal
Helly chordal ∩ clique-chordal
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
1,4
,diamond)-free
K
1,4
-free
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-free
(K
2
∪ K
3
,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
,co-diamond)-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
,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
3,3,3
,
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
,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
,co-gem)-free
(K
4
,odd anti-hole,odd-hole)-free
K
4
-free
K
4
-free ∩ perfect
(K
5
- e,S
3
,
3K
2
,
A
,
C
4
∪ 2K
1
,
E
,
P
2
∪ P
3
,
R
,claw,co-twin-house,odd-hole)-free
(K
5
- e,W
5
,
A
,
C
4
∪ 2K
1
,
P
2
∪ P
3
,
R
,claw,co-twin-C
5
,co-twin-house)-free
(K
5
- e,
A
,
C
4
∪ 2K
1
,
P
2
∪ P
3
,
R
,claw,co-twin-house,odd-hole)-free
K
5
-free
K
6
-free
K
7
-free
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N
*
(P,P
5
)-free
(P,P
7
)-free
(P,P
8
)-free
(P,T
2
)-free
(P,co-fork)-free
(P,star
1,2,3
)-free
(P,star
1,2,4
)-free
(P,star
1,2,5
)-free
P-free
(P
2
∪ P
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
-free
P
4
-bipartite
P
4
-brittle
P
4
-comparability
P
4
-laden
(P
5
,X
82
,X
83
)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free
(P
5
,
P
,anti-hole)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,
P
6
,anti-hole)-free
(P
5
,
P
6
)-free
(P
5
,
P
6
)-free ∩ weakly chordal
(P
5
,
X
38
,co-gem)-free
(P
5
,anti-hole,co-bicycle,co-domino)-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,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
,house)-free
P
5
-free
P
5
-free ∩ weakly chordal
(P
6
,X
10
,X
11
,X
12
,X
13
,X
14
,X
15
,X
5
,X
6
,X
7
,X
8
,X
9
,
C
6
,
P
6
,antenna,hole)-free
(P
6
,X
30
,X
8
)-free
(P
6
,claw)-free
(P
6
,hole,house)-free
(P
6
,house)-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
,
3K
2
,
E
,odd-hole)-free ∩ line
(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
S
3
-free ∩ chordal
V-perfect
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,odd-hole)-free
(W
4
,claw,gem)-free
(W
4
,claw)-free
(W
4
,gem)-free
(W
4
,gem)-free ∩ short-chorded
Welsh-Powell opposition
Welsh-Powell perfect
W
n+4
-free
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X
12
,X
5
,X
95
,X
96
,X
97
,
X
12
,
X
5
,
X
95
,
X
96
,
X
97
,
claw ∪ triangle
,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X
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
79
,X
80
)-free ∩ modular
(X
91
,claw)-free
XC
10
-free
XC
13
-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
β-perfect ∩ perfect
(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+4
,
X
59
,co-longhorn)-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
,
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
,odd anti-cycle)-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
,co-diamond)-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
,fork)-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-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
30
,
XZ
1
,
XZ
4
,co-longhorn)-free
(
X
79
,
X
80
)-free
(
X
82
,
X
83
,house)-free
(
X
91
,co-claw)-free
XC
10
-free
XC
13
-free
(n+4)-pan
-free
odd-cycle ∪ K
1
-free
absolute bipartite retract
absolutely perfect
absorbantly perfect
all-4-simplicial
almost claw-free
almost-split
alternately colourable
alternately orientable
alternation
(anti-hole,bull,odd-hole)-free
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
(anti-hole,odd-hole)-free
anti-hole-free
b-perfect
b-perfect ∩ chordal
balanced
balanced 2-interval
balanced ∩ chordal
balanced ∩ line
balanced ∩ paw-free
basic perfect
biclique separable
biclique-Helly
bip
*
bipartite
bipartite ∩ co-perfectly orderable
bipartite ∩ weakly chordal
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ double split ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ split
biplanar
bisplit
bisplit ∩ triangle-free
bitolerance
bounded bitolerance
bounded multitolerance
bridged
bridged ∩ clique-Helly
brittle
building-free
building-free ∩ even-signable
building-free ∩ odd-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
bull-free ∩ strict quasi-parity
(butterfly,claw)-free
(butterfly,gem)-free
caterpillar arboricity <= 2
charming
chordal
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ dually chordal
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal bipartite
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular perfect
circular strip
circular trapezoid
(claw,diamond,odd-hole)-free
(claw,diamond)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ perfect
claw-free ∩ upper domination perfect
clique graphs
clique separable
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
clique-perfect
clique-perfect ∩ triangle-free
co-2-subdivision
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P
4
-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-β-perfect
co-biclique separable
co-bipartite
co-building-free
(co-butterfly,co-claw)-free
(co-butterfly,co-gem)-free
co-chordal
co-circular perfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(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-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension d
(co-cricket,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-domino-free
(co-fork,hole)-free
(co-fork,house)-free
co-fork-free
co-gem-free
co-hereditary clique-Helly
co-interval filament
co-interval mixed
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-quasi-line
co-strongly chordal
co-sun-free
co-trapezoid
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
comparability
comparability ∩ weakly chordal
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
containment graphs
cop-win
cycle-bicolorable
d-trapezoid
diametral path
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
disk-Helly
dismantlable
domination
domination perfect
domination perfect ∩ triangle-free
domino
(domino,gem,house)-free
domino-free
doubled
doubly chordal
dually chordal
even anti-cycle-free
even anti-hole-free
even-cycle-free
even-hole-free
even-hole-free ∩ probe chordal
even-signable
extended P
4
-laden
(fork,house)-free
fork-free
gem-free
generalized split
generalized strongly chordal
girth >=9
good
gridline
half-disk Helly
hereditary Helly
hereditary Matula perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary biclique-Helly
hereditary clique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary disk-Helly
hereditary dismantlable
hereditary dominating pair
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary modular
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary perfect elimination bipartite
hereditary sat
hereditary weakly modular
(hole,odd anti-hole)-free
(hole,odd-cycle)-free
hole-free
homogeneously orderable
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
induced-hereditary pseudo-modular
interval filament
irredundance perfect
irredundance perfect with ir(G)<= 4
isometric-HH-free
isometric-hereditary pseudo-modular
k-SEG
kernel solvable
line
line ∩ perfect
line graphs of Helly hypergraphs of rank 3
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of linear Helly hypergraphs of rank 3
line graphs of multigraphs without triangles
line graphs of triangle-free graphs
linear domino
locally bipartite
locally chordal
locally perfect
locally split
maxibrittle
maximal clique irreducible
modular
modular ∩ open-neighbourhood-Helly
monopolar
multitolerance
murky
(n+4)-pan-free
nK
2
-free, fixed n
nP
3
-free, fixed n
nearly bipartite
neighbourhood chordal
neighbourhood perfect
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
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-signable
odd-sun-free
open-neighbourhood-Helly
opposition
outer-string
(p,q<=2)-colorable
p-connected
parity
partial rectangle visibility
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
power-chordal
preperfect
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe AT-free
probe Gallai
probe HHDS-free
probe Meyniel
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-bipartite
probe co-comparability
probe comparability
probe diamond-free
probe split
probe strongly chordal
pseudo-modular
pseudo-modular ∩ triangle-free
pseudo-split
quasi-Meyniel
quasi-brittle
quasi-line
quasi-parity
quasitriangulated
rectangle visibility
rigid circuit
self-complementary
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
spider graph
split
split-neighbourhood
split-perfect
starlike
strict quasi-parity
strictly clique irreducible
string
strong asteroid free
strong domination perfect
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly even-signable
strongly orderable
strongly perfect
substar
subtree filament
subtree overlap
sun-free
sun-free ∩ weakly chordal
superbrittle
superperfect
thickness <= 2
totally unimodular
trapezoepiped
trapezoid
tree convex
triangle-free
triangulated
tripartite
unimodular
unipolar
unit 2-circular arc
unit 2-interval
unit 3-interval
upper domination perfect
upper irredundance perfect
very strongly perfect
visibility
weak bipolarizable
weak bisplit
weak dominating pair
weak rectangle visibility
weakly bridged
weakly chordal
weakly geodetic
weakly modular
well covered
well-partitioned chordal
back to top
NP-hard
back to top
NP-complete
back to top
coNP-complete
back to top
Open
back to top
Unknown to ISGCI
(0,2)-graph
(0,2)-graph ∩ bipartite
1-bounded tripartite
1-string
2-DIR
2-connected
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-connected ∩ (P
6
,claw)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-edge-connected
2-strongly regular
2-strongly regular ∩ planar
2-subdivision ∩ planar
2-thin
2-threshold
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
,
H
,
K
1,4
,
X
85
)-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
,C
4
,C
5
,S
3
,net)-free
(2K
2
,C
4
,C
5
,co-sun)-free
(2K
2
,C
4
,C
5
,sun)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
(2K
2
,
C
6
,odd anti-cycle)-free
(2K
2
,
X
91
,co-claw)-free
(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,R,X
168
,X
171
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,
A
,
C
6
,
E
,
H
,
R
,
X
168
,
X
171
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K
3
+ e,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,3K
1
,
A
,
H
,
T
2
,
X
18
,
X
45
,co-domino)-free
(2P
3
,triangle)-free
(2P
4
,A,C
5
,C
6
,C
7
,E,K
3,3
-e,P
7
,R,X
1
,X
103
,X
5
,X
58
,X
84
,X
98
,
C
6
,
P
6
,
X
5
,
sunlet
4
,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
3-DIR
3-DIR contact
(3K
1
,C
5
,K
3
∪ K
4
,
BW
3
,
K
3,4
-e
,
T
2
,
X
18
,
X
92
,
X
93
)-free
(3K
1
,
2P
3
)-free
(3K
1
,
3K
2
)-free
(3K
1
,
E
)-free
(3K
1
,
K
1,5
)-free
(3K
1
,
P
2
∪ P
4
)-free
(3K
1
,
T
2
,
X
2
,
X
3
,anti-hole)-free
(3K
1
,
XC
12
)-free
(3K
1
,co-cross)-free
(3K
2
,triangle)-free
3d grid
(4-fan,C
n+4
,K
5
- e,S
3
,X
100
,X
101
,X
102
,
H
,
K
3
∪ 2K
1
)-free
(4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
4-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
,co-claw,co-diamond)-free
(4K
1
,house)-free
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular
5-regular ∩ hamiltonian
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,3)
(7,5)
(A,C
5
,C
6
,E,P
6
,S
3
,X
159
,X
219
,X
5
,X
58
,
A
,
C
6
,
E
,
P
6
,
X
159
,
X
219
,
X
5
,
X
58
,antenna,co-antenna,co-domino,co-rising sun,domino,net,rising sun)-free
(A,C
5
,C
6
,E,P
6
,S
3
,X
159
,X
219
,X
58
,
A
,
X
159
,
X
219
,co-rising sun,domino,house,net,rising sun)-free
(A,C
5
,P
5
,S
3
,X
159
,X
219
,
A
,
C
6
,
E
,
P
6
,
X
159
,
X
219
,
X
58
,co-domino,co-rising sun,net,rising sun)-free
(A,E,S
3
,X
1
,domino,hole,house,net,rising sun)-free
(A,H,K
3,3
,K
3,3
-e,T
2
,X
18
,X
45
,domino,triangle)-free
(A,P
6
,clique wheel,domino,hole,house)-free
AT-free ∩ bipartite
B
0
-CPG
B
0
-VPG
B
0
-VPG ∩ bipartite
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
B
0
-VPG ∩ triangle-free
B
1
-CPG
B
1
-CPG ∩ 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
,H,K
1,4
,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 ∩ maximum degree 3 ∩ planar
(C
4
,C
5
,K
4
,diamond)-free ∩ 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
,K
4
,claw,diamond)-free
(C
4
,X
91
,claw)-free
(C
4
,triangle)-free ∩ planar
C
4
-free ∩ C
6
-free ∩ bipartite
(C
5
,C
6
,C
7
,C
8
,P
8
,X
19
,X
20
,X
21
,X
22
,gem,house)-free
(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
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
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free ∩ co-line
(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
CIS
CPG
(C
n+3
∪ K
1
,diamond,paw)-free
(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
,net)-free
(C
n+4
,T
2
,XF
2
n+1
)-free
(C
n+4
,T
2
,net)-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+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
D
Delaunay
Deza
Dilworth 3
Dilworth 4
(E,triangle)-free
E-free ∩ planar
EPT ∩ chordal
F
n
grid
Gabriel
(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
Hamilton-connected
Hamming
Helly ∩ reflexive
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly circle
Helly circular arc
Helly circular arc ∩ (
C
7
,odd-hole)-free
Helly circular arc ∩ concave-round
Helly circular arc ∩ perfect
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
Helly subtree
Hilbertian
H
n,q
grid
(K
1,4
,odd-cycle)-free
(K
1,4
,odd-cycle)-free ∩ planar
(K
1,4
,paw)-free
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
(K
1,5
,triangle)-free
(K
2
∪ K
3
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2,3
,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
3,3
,K
5
)-minor-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
,odd anti-hole,odd-hole)-free ∩ dually chordal
K
4
-free ∩ dually chordal ∩ perfect
K
4
-free ∩ map
K
4
-free ∩ planar
Laman
Laman ∩ planar
Mycielski
N
*
-perfect
(P
2
∪ P
4
,triangle)-free
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
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
P
5
-free ∩ tripartite
P
6
-free ∩ tripartite
(P
7
,odd-cycle)-free
P
7
-free ∩ bipartite
PI
PI
*
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
,
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)-free
(S
3
,
C
n+4
,net)-free
(S
3
,net)-free ∩ chordal
(S
3
,net)-free ∩ split
SEG
(T
2
,X
2
,X
3
,hole,triangle)-free
(T
2
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
Urquhart
(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
37
,diamond,even-cycle)-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
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
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
3
-perfect
(
C
n+3
∪ K
1
,co-diamond,co-paw)-free
(
C
n+4
,
H
)-free
(
C
n+4
,
T
2
,co-XF
2
n+1
)-free
(
C
n+4
,co-claw)-free
(
K
1,4
,co-paw)-free
(
K
1,4
,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
(
X
37
,co-diamond,even anti-cycle)-free
(
XC
11
,co-claw,co-diamond)-free
(
XC
11
,odd anti-cycle)-free
XC
11
-free
XC
12
-free
τ
k
-perfect for all k >= 2
absolute reflexive retract
adjoint
adjoint ∩ partial directed line
almost CIS
almost median
alternately orientable ∩ co-comparability
apex
balanced ∩ co-line
bar visibility
basic 4-leaf power
biconvex
bigeodetic
binary Hamming
bipartable
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ co-comparability
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ girth >=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ grid intersection
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ unit grid intersection
bipartite permutation
bipartite tolerance
bipolarizable
bithreshold
book thickness 2
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded tolerance
bounded treewidth
boxicity 2
boxicity 2 ∩ co-bipartite
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ domination perfect
chordal ∩ hamiltonian
chordal ∩ hereditary dominating pair
chordal ∩ proper circular arc
chordal-perfect
circle
circle ∩ diamond-free
circle graph with equator
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 convex bipartite
circular interval
circular permutation
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ normal Helly circular arc
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ well covered
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
clique-Helly ∩ dismantlable ∩ reflexive
co-biconvex
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bounded tolerance
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2, height 2
(co-diamond,even anti-cycle)-free
co-forest-perfect
co-interval bigraph
co-interval containment bigraph
co-leaf power
co-planar
co-proper interval bigraph
co-threshold tolerance
co-tolerance
coin
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, height 2
complete Hamming
concave-round
containment graph of circles
containment graph of intervals
containment graphs of circular arcs
convex
convex-round
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cubical
(diamond,even-cycle)-free
directed line
directed path
disk
disk contact
distance regular
distance regular of diameter 2
domination perfect ∩ planar
double split
dually chordal ∩ tripartite
edge regular
equimatchable
forest-perfect
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
galled-tree explainable
galled-tree explainable ∩ house-free
generically minimally rigid
genus 0
genus 1
geodetic
graceful
grid
grid graph
grid graph ∩ maximum degree 3
grid intersection
hamiltonian
hamiltonian ∩ planar
hamiltonian ∩ split
harmonious
hereditary N
*
-perfect
hereditary clique-Helly ∩ self-clique
hereditary median
hole-free ∩ planar
homothetic triangle contact
hypercube
intersection graphs of parallelograms (squares)
interval bigraph
interval containment bigraph
interval enumerable
interval regular
interval regular of diameter 2
irredundance perfect with ir(G)=2
isometric subgraph of a hypercube
k-DIR
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
leaf power
leaf power ∩ min leaf power
leaf power ∪ min leaf power
line ∩ mock threshold
line ∩ well covered
line graphs of planar cubic bipartite graphs
line perfect
linear arboricity <= 2
linear domino ∩ maximum degree 4
linearly convex triangular grid graph
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
map
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
min leaf power
mock threshold
mock threshold ∩ split
module-composed
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal Helly circular arc
normal circular arc
odd-hole-free ∩ planar
odd-signable ∩ triangle-free
overlap
(p,q)-colorable
(p,q)-split
p-tree
pairwise compatibility
parallelepiped
partial 3d grid
partial bar visibility
partial cube
partial directed line
partial grid
partitionable
penny
perfect ∩ planar
permutation
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
premedian
probe interval
probe interval bigraph
probe permutation
probe proper interval
probe unit interval
proper Helly circular arc
proper chordal
proper circular arc
proper interval bigraph
proper tolerance
pseudo-median
pseudo-median ∩ triangle-free
(q,t)
quasi-adjoint
quasi-median
rectagraph
rectangle intersection
reflexive
relative neighbourhood graph
rooted directed path
self-clique
semi-median
semi-square intersection
solid grid graph
solid triangular grid graph
split ∩ strongly chordal
square of tree
star convex
strict 2-threshold
strict B
1
-VCPG
strongly brittle
strongly odd-signable
strongly regular
subhamiltonian
threshold tolerance
tolerance
tolerance ∩ triangle-free
toroidal
tree-perfect
triad convex
triangle contact
triangular grid graph
unbreakable
undirected path
unigraph
unit 2-circular track
unit 2-track
unit 3-circular track
unit 3-track
unit Helly circle
unit Helly circular arc
unit bar visibility
unit circular arc
unit disk
unit grid intersection
unit interval bigraph
unit square
unit tolerance
universally signable
walk regular
weak bar visibility
weakly median
well-dominated
wing-triangulated
back to top
(G)-perfect
3-perfect