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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Graph isomorphism
Definition:
Input: Graphs
G
and
H
in this class
Output: True iff
G
and
H
are isomorphic.
Linear
(0,2)-colorable ∩ chordal
(0,3)-colorable ∩ chordal
1-DIR
(2,0)-colorable ∩ chordal
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-leaf power
2-outerplanar
2-strongly regular ∩ planar
2-subdivision ∩ planar
2-terminal series-parallel
2-tree
2-tree ∩ probe interval
(2C
4
,3K
2
,C
6
,E,P
2
∪ P
4
,P
6
,X
25
,X
26
,X
27
,X
28
,X
29
,odd-cycle)-free
2K
1
-free
(2K
2
,3K
1
,C
4
,P
4
)-free
(2K
2
,3K
1
,P
3
)-free
(2K
2
,C
4
,C
5
,H,S
3
,X
160
,
X
159
,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,X
159
,X
160
,
H
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,S
3
,claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,net,rising sun)-free
(2K
2
,C
4
,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 ∩ 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
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
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(4K
1
,P
4
)-free
5-leaf power ∩ distance-hereditary
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,2)
AC
AT-free ∩ bipartite
AT-free ∩ chordal
Apollonian network
B
1
-CPG ∩ triangle-free
(C
4
,C
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free ∩ planar
(C
4
,C
5
,C
6
,C
7
,C
8
)-free ∩ maximum degree 3 ∩ planar
(C
4
,C
5
,K
4
,diamond)-free ∩ planar
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free ∩ planar
(C
4
,P
4
,dart)-free
(C
4
,P
4
,diamond,paw)-free
(C
4
,P
4
)-free
(C
4
,
P
3
,triangle)-free
(C
4
,
P
3
)-free
(C
4
,triangle)-free ∩ planar
C
4
-free ∩ co-comparability
(C
5
,P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
C
5
-free ∩ P
4
-extendible
(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
,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
,K
4
)-free
(C
n+4
,P
5
,bull)-free
(C
n+4
,P
5
,claw,gem)-free
(C
n+4
,S
3
∪ K
1
,claw,net)-free
(C
n+4
,S
3
,claw,net)-free
(C
n+4
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-free
(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
Delaunay
Dilworth 1
Dilworth 2
E-free ∩ planar
Gabriel
Halin
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
H
n,q
grid
(K
1,4
,odd-cycle)-free ∩ planar
(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
3,3
,K
5
)-minor-free
K
3
-minor-free
(K
4
,P
4
)-free
K
4
-free ∩ map
K
4
-free ∩ planar
K
4
-minor-free
Laman ∩ planar
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
(S
3
,claw,net)-free ∩ chordal
SC 2-tree
SC 3-tree
(T
2
,X
2
,X
3
,hole,triangle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
Urquhart
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
(XC
11
,odd-cycle)-free ∩ planar
(XC
12
,cycle)-free
(XC
12
,triangle)-free ∩ planar
(
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
(
C
n+4
,bull,house)-free
(
P
3
,triangle)-free
P
3
-free
(
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,even anti-hole,odd anti-cycle)-free
(
T
2
,co-cycle)-free
(
T
3
,
X
81
,co-cycle)-free
(
T
3
,co-cycle)-free
almost tree (1)
astral triple-free
bar visibility
binary tree
binary tree ∩ partial grid
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ cubic ∩ planar
bipartite ∩ girth>=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ planar
bipartite ∩ trapezoid
bipartite chain
bipartite permutation
bipartite tolerance
block
block duplicate
book thickness 2
boxicity 1
cactus
caterpillar
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 ∩ proper circular arc
chordal ∩ unit circular arc
circle graph with equator
circular arc ∩ co-bipartite
circular arc ∩ cograph
circular interval
(claw,odd-cycle)-free
claw-free ∩ interval
claw-free ∩ normal Helly circular arc
clique graphs of Helly circular arc
clique graphs of interval
clique graphs of normal Helly circular arc
cliquewidth 2
cluster
co-biconvex
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-cluster
co-comparability ∩ comparability
co-comparability graphs of posets of interval dimension 2, height 2
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-interval bigraph
co-interval containment bigraph
co-probe threshold
co-proper interval bigraph
co-trivially perfect
co-trivially perfect ∩ trivially perfect
cograph
cograph ∩ interval
cograph ∩ split
coin
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
concave-round
containment graph of intervals
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cycle-free
difference
disjoint union of stars
disk contact
domination perfect ∩ planar
domishold
genus 0
grid
grid graph
grid graph ∩ maximum degree 3
half
hamiltonian ∩ interval
hamiltonian ∩ planar
hole-free ∩ planar
homogeneously representable
homothetic triangle contact
indifference
indifference ∩ split
intersection graph of nested intervals
interval
k-outerplanar
line graphs of acyclic multigraphs
line graphs of planar cubic bipartite graphs
linear NLC-width 1
linear cliquewidth 2
linear interval
linearly convex triangular grid graph
lobster
locally connected ∩ triangular grid graph
maximal outerplanar
maximal planar
maximum degree 1
maximum degree 3 ∩ planar ∩ triangle-free
median ∩ planar
normal Helly circular arc
odd-hole-free ∩ planar
outerplanar
partial 2-tree
partial 3-tree ∩ planar
partial bar visibility
partial grid
perfect ∩ planar
permutation
permutation ∩ split
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
probe block
probe co-trivially perfect ∩ probe trivially perfect
probe complete
probe interval ∩ tree
probe threshold
probe threshold ∩ split
proper Helly circular arc
proper circular arc
proper interval
proper interval bigraph
ptolemaic
ptolemaic ∩ weakly geodetic
quasi-threshold
relative neighbourhood graph
restricted block duplicate
semicircular
series-parallel
solid grid graph
solid triangular grid graph
split ∩ threshold signed
starlike threshold
strict B
1
-VCPG
strictly chordal
subhamiltonian
superfragile
thick tree
threshold
threshold signed
tolerance ∩ tree
tree
treewidth 2
triangle contact
triangular grid graph
trivially perfect
unicyclic
unit Helly circular arc
unit bar visibility
unit circular arc
unit interval
unit interval bigraph
weak bar visibility
back to top
Polynomial
1-bounded bipartite
2-bounded bipartite
(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
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,co-claw,co-diamond)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
2K
2
-free ∩ probe cograph
3-tree
(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
,
K
1,5
)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
6
)-free
(3K
1
,
X
172
)-free
(3K
1
,
XC
12
)-free
(3K
1
,co-fork)-free
(3K
1
,house)-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
3d grid
4-leaf power
4-regular
4-regular ∩ hamiltonian
(4K
1
,K
4
)-free
(4K
1
,
C
n+4
)-free
(4K
1
,co-claw,co-diamond)-free
(5,1)
(5,2)-crossing-chordal
5-leaf power
5-regular
5-regular ∩ hamiltonian
(6,2)-chordal ∩ bipartite
(7,3)
(7,4)
(8,4)
(9,6)
(A,T
2
,odd-cycle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,K
1,4
,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,X
85
,triangle)-free ∩ 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
,XC
11
,claw,diamond)-free
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free
(C
4
,K
4
,claw,diamond)-free
(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
,
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
-tidy
C
5
-free ∩ matrogenic
(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
(E,odd-cycle)-free
E-free ∩ bipartite
F
n
grid
HHDG-free
(K
1,4
,odd-cycle)-free
(K
1,5
,triangle)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2
∪ claw,triangle)-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-free
(K
4
,claw,diamond)-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
(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
4
-extendible
P
4
-lite
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
,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
,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
,co-claw,net)-free
(S
3
,net)-free ∩ extended P
4
-sparse
SC k-tree, fixed k
(T
2
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
(X
172
,triangle)-free
(X
177
,odd-cycle)-free
(XC
11
,claw,diamond)-free
(XC
11
,odd-cycle)-free
(XC
12
,triangle)-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
(
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
,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
(
K
1,4
,odd anti-cycle)-free
(
P
,butterfly,fork,gem)-free
(
P
,fork,gem)-free
(
P
,fork,house)-free
(
P
7
,
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
P
7
,
star
1,2,3
,odd anti-cycle)-free
(
X
177
,odd anti-cycle)-free
(
XC
11
,co-claw,co-diamond)-free
(
XC
11
,odd anti-cycle)-free
XC
11
-free
(
XC
12
,co-cycle)-free
XC
12
-free
(
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
(anti-hole,co-domino,odd anti-cycle)-free
bi-cograph
biconvex
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ distance-hereditary
bipartite ∩ maximum degree 3
bipartite ∩ module-composed
bipartite ∩ probe interval
bipartite ∩ tolerance
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(claw ∪ 3K
1
,odd-cycle)-free
(claw,co-claw)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
cliquewidth 3
cliquewidth 4
co-bithreshold ∩ split
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
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 ∪ interval
(co-paw,paw)-free
(co-paw,triangle)-free
co-planar
co-probe cograph
comparability ∩ distance-hereditary
comparability ∩ split
comparability graphs of posets of interval dimension 2, height 2
comparability graphs of semiorders
convex
convex-round
cubic
cubic ∩ hamiltonian
distance-hereditary
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
extended P
4
-reducible
extended P
4
-sparse
(fork,odd-cycle)-free
(fork,triangle)-free
genus 1
independent module-composed
interval bigraph
interval containment bigraph
k-path graph, fixed k
k-tree, fixed k
linear arboricity <= 2
linear domino ∩ maximum degree 4
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
matrogenic
matroidal
maximum degree 3
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
minimally imperfect
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
partial 3-tree
partial 3d grid
partial 4-tree
partial k-tree, fixed k
partner-limited
probe P
4
-reducible
probe P
4
-sparse
probe bipartite chain
probe bipartite distance-hereditary
probe co-trivially perfect
probe cograph
probe distance-hereditary
probe ptolemaic
probe trivially perfect
proper chordal
(q, q-3), fixed q>= 7
(q,q-4), fixed q
semi-P
4
-sparse
split ∩ superperfect
strong tree-cograph
tolerance ∩ triangle-free
toroidal
tree-cograph
treewidth 3
treewidth 4
treewidth 5
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
(2,2)-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
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
4
-simplicial
(P
5
,X
82
,X
83
)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,anti-hole,co-bicycle,co-domino)-free
(P
5
,anti-hole,co-domino,co-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
-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
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+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
(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 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
universally signable
upper domination perfect
upper irredundance perfect
very strongly perfect
visibility
weak bipolarizable
weak bisplit
weak dominating pair
weak rectangle visibility
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
circular arc
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-edge-connected
2-strongly regular
2-thin
2-threshold
(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
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
,
P
2
∪ P
4
)-free
(3K
1
,co-cross)-free
(3K
2
,triangle)-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
(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
,house)-free
(6,3)
(7,5)
(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
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
-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
6
,odd-cycle)-free
(C
4
,X
91
,claw)-free
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
CIS
CPG
(C
n+3
∪ K
1
,diamond,paw)-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
,H)-free
(C
n+4
,S
3
∪ K
1
,
X
103
,claw,eiffeltower,net ∪ K
1
)-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
D
Deza
Dilworth 3
Dilworth 4
(E,triangle)-free
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
Hamilton-connected
Hamming
Helly ∩ reflexive
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly circle
Helly subtree
Hilbertian
(K
1,4
,paw)-free
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
(K
2
∪ K
3
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2,3
,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
,odd anti-hole,odd-hole)-free ∩ dually chordal
K
4
-free ∩ dually chordal ∩ perfect
Laman
Mycielski
N
*
-perfect
(P
2
∪ P
4
,triangle)-free
P
4
-indifference
(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
,
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
(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
(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
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
cal P
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
(
P
7
,odd anti-cycle)-free
(
X
37
,co-diamond,even anti-cycle)-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
basic 4-leaf power
bigeodetic
binary Hamming
bipartable
bipartite ∩ boxicity 2
bipartite ∩ grid intersection
bipartite ∩ mock threshold
bipartite ∩ quasi-median
bipartite ∩ unit grid intersection
bipolarizable
bithreshold
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-perfect
circle
circle ∩ diamond-free
circular arc ∩ clique-Helly
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular convex bipartite
circular permutation
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ well covered
clique-Helly ∩ dismantlable ∩ reflexive
co-bithreshold
co-bounded tolerance
co-comparability ∩ tolerance
co-comparability graphs of dimension d posets
(co-diamond,even anti-cycle)-free
co-forest-perfect
co-leaf power
co-threshold tolerance
co-tolerance
comparability graphs of dimension 3 posets
comparability graphs of dimension 4 posets
comparability graphs of dimension d posets
complete Hamming
containment graph of circles
containment graphs of circular arcs
(cross,triangle)-free
cubical
(diamond,even-cycle)-free
directed line
directed path
disk
distance regular
distance regular of diameter 2
double split
dually chordal ∩ tripartite
edge regular
equimatchable
forest-perfect
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
generically minimally rigid
geodetic
graceful
grid intersection
hamiltonian
hamiltonian ∩ split
harmonious
hereditary N
*
-perfect
hereditary clique-Helly ∩ self-clique
hereditary median
hypercube
intersection graphs of parallelograms (squares)
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 perfect
locally connected
map
max-tolerance
median
middle
min leaf power
mock threshold
mock threshold ∩ split
module-composed
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal circular arc
odd-signable ∩ triangle-free
overlap
(p,q)-colorable
(p,q)-split
p-tree
pairwise compatibility
parallelepiped
partial cube
partial directed line
partitionable
premedian
probe interval
probe interval bigraph
probe permutation
probe proper interval
probe unit interval
proper tolerance
pseudo-median
pseudo-median ∩ triangle-free
(q,t)
quasi-adjoint
quasi-median
rectagraph
rectangle intersection
reflexive
rooted directed path
self-clique
semi-median
semi-square intersection
split ∩ strongly chordal
square of tree
star convex
strict 2-threshold
strongly odd-signable
strongly regular
threshold tolerance
tolerance
tree-perfect
triad convex
unbreakable
undirected path
unigraph
unit 2-circular track
unit 2-track
unit 3-circular track
unit 3-track
unit Helly circle
unit disk
unit grid intersection
unit tolerance
walk regular
weakly median
well-dominated
wing-triangulated
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