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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Feedback vertex set
Definition:
Input:
A graph
G
in this class and an integer
k
.
Output:
True iff
G
contains a set
S
of vertices, with |
S
| <=
k
, such that every cycle in
G
contains a vertex from
S
.
Linear
(0,2)-colorable ∩ chordal
1-DIR
1-bounded bipartite
(2,0)-colorable ∩ chordal
2-leaf power
(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
,C
5
,co-claw,co-diamond)-free
(2K
2
,C
4
,P
4
,triangle)-free
(2K
2
,C
4
,P
4
)-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
)-free
2K
2
-free ∩ bipartite
(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
(3K
1
,C
4
,C
5
)-free
(3K
1
,C
4
,
P
3
)-free
(3K
1
,C
5
,butterfly,diamond)-free
(3K
1
,P
3
)-free
(3K
1
,P
4
)-free
(3K
1
,
P
3
)-free
(3K
1
,co-fork)-free
(3K
1
,house)-free
(3K
1
,paw)-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
(4K
1
,K
4
)-free
(4K
1
,P
4
)-free
(5,1)
(5,2)-crossing-chordal
5-leaf power ∩ distance-hereditary
(6,2)
(6,2)-chordal ∩ bipartite
(7,3)
(7,4)
(8,4)
(9,6)
AC
AT-free ∩ bipartite
AT-free ∩ chordal
(C
4
,P
4
,dart)-free
(C
4
,P
4
)-free
(C
4
,
P
3
,triangle)-free
(C
4
,
P
3
)-free
C
4
-free ∩ co-comparability
(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
,S
3
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
3K
2
,
P
2
∪ P
4
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free ∩ P
4
-tidy
(C
5
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,co-butterfly,co-diamond,triangle)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
(C
n+4
,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
HHDG-free
(K
2
∪ K
3
,P
4
,butterfly)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
2,3
,P
4
,co-butterfly)-free
K
2
-free
K
3
-minor-free
(K
4
,P
4
)-free
NLCT-width 1
(P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(P,P
5
,
P
,co-fork,fork,house)-free
(P,
P
,co-fork,fork)-free
(P
3
,triangle)-free
P
3
-free
(P
4
,
2P
3
)-free
(P
4
,co-cycle)-free
(P
4
,cycle)-free
(P
4
,triangle)-free
P
4
-extendible
P
4
-extendible ∩ P
4
-sparse
P
4
-free
P
4
-lite
P
4
-reducible
P
4
-sparse
P
4
-tidy
P
4
-tidy ∩ (S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
P
4
-tidy ∩ balanced
P
4
-tidy ∩ hereditary clique-Helly ∩ perfect
P
4
-tidy ∩ perfect
(P
5
,bull,house)-free
(P
5
,bull)-free ∩ interval
(P
5
,co-fork,house)-free
(P
5
,diamond)-free
(P
5
,fork,house)-free
(P
5
,triangle)-free
P
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
,claw,net)-free ∩ chordal
(S
3
,net)-free ∩ extended P
4
-sparse
(T
2
,X
2
,X
3
,hole,triangle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
(XC
12
,cycle)-free
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
(
C
n+4
,bull,house)-free
(
C
n+4
,co-claw,co-gem,house)-free
(
P
,butterfly,fork,gem)-free
(
P
,fork,gem)-free
(
P
,fork,house)-free
(
P
3
,triangle)-free
P
3
-free
astral triple-free
bi-cograph
binary tree
binary tree ∩ partial grid
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ distance-hereditary
bipartite ∩ module-composed
bipartite ∩ trapezoid
bipartite chain
bipartite permutation
bipartite tolerance
block
block duplicate
boxicity 1
(bull,co-fork,fork)-free
(bull,fork,gem)-free
(bull,fork,house)-free
caterpillar
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ co-comparability
chordal ∩ cograph
chordal ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ domino
chordal ∩ gem-free
chordal ∩ probe diamond-free
chordal ∩ unit circular arc
circular arc ∩ cograph
(claw,co-claw)-free
(claw,odd-cycle)-free
(claw,paw)-free
claw-free ∩ interval
clique graphs of interval
cliquewidth 2
cluster
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
(co-diamond,diamond)-free
(co-fork,odd anti-cycle)-free
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
(co-paw,paw)-free
(co-paw,triangle)-free
co-probe threshold
co-trivially perfect
co-trivially perfect ∩ trivially perfect
cograph
cograph ∩ interval
cograph ∩ split
comparability ∩ distance-hereditary
comparability graphs of arborescence orders
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete
complete bipartite
complete multipartite
complete split
cycle-free
difference
disjoint union of stars
distance-hereditary
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
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
line graphs of acyclic multigraphs
linear NLC-width 1
linear cliquewidth 2
linear interval
lobster
matrogenic
matroidal
maximum degree 1
minimally imperfect
partner-limited
permutation ∩ split
probe block
probe complete
probe interval ∩ tree
probe threshold ∩ split
proper interval
proper interval bigraph
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
split ∩ threshold signed
strictly chordal
superfragile
thick tree
threshold
tolerance ∩ tree
tree
trivially perfect
unit interval
unit interval bigraph
back to top
Polynomial
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar ∩ chordal
(2,0)-colorable
(2,2)-colorable ∩ chordal
2-bounded bipartite
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-connected ∩ cubic ∩ planar
2-outerplanar
2-terminal series-parallel
2-tree
2-tree ∩ probe interval
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
,
H
,
K
1,4
,
X
85
)-free
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
,
H
,
X
85
)-free
(2K
2
,3K
1
,C
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,3K
1
)-free
(2K
2
,4K
1
,C
5
,co-diamond)-free
(2K
2
,4K
1
,co-claw,co-diamond)-free
(2K
2
,5K
1
,C
5
,K
3
∪ 2K
1
,P
3
∪ 2K
1
,
C
6
,
C
7
,
C
8
,
K
1,4
,
K
5
- e
,claw ∪ K
1
,co-butterfly,co-cricket,co-dart,co-gem)-free
(2K
2
,A,H)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net)-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
4
,C
5
)-free
(2K
2
,C
4
)-free
(2K
2
,C
5
,S
3
,X
159
,X
160
,X
161
,X
162
,X
46
,X
70
,
2P
3
,
3K
2
,
H
,
P
2
∪ P
4
,
X
1
,co-rising sun,house,net)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,C
5
,
C
6
,net)-free
(2K
2
,C
5
,
T
2
)-free
(2K
2
,C
5
)-free
(2K
2
,
2P
3
,
C
6
)-free
(2K
2
,
C
6
,
C
8
,
K
1,4
,odd anti-cycle)-free
(2K
2
,
C
6
,odd anti-cycle)-free
(2K
2
,
P
6
)-free
(2K
2
,
X
91
,co-claw)-free
(2K
2
,claw)-free
(2K
2
,co-claw,co-diamond)-free
(2K
2
,co-diamond)-free
(2K
2
,house)-free
(2K
2
,net)-free
(2K
2
,odd anti-hole)-free
2K
2
-free
2K
2
-free ∩ probe cograph
2K
2
-free ∩ probe trivially perfect
(2K
3
+ e,3K
1
,C
5
,
T
2
,
X
18
,
X
94
,co-domino)-free
(2K
3
,2K
3
+ e,3K
1
,
A
,
H
,
T
2
,
X
18
,
X
45
,co-domino)-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
3-tree
3-tree ∩ planar
(3K
1
,C
5
,K
3
∪ K
4
,
BW
3
,
K
3,4
-e
,
T
2
,
X
18
,
X
92
,
X
93
)-free
(3K
1
,C
5
,K
5
- e,
C
6
∪ K
1
,
C
7
,
K
3,3
∪ K
1
,
K
3,3
-e ∪ K
1
,
domino ∪ K
1
)-free
(3K
1
,C
5
,
C
6
,
P
6
)-free
(3K
1
,C
5
,
C
6
,
X
164
,
X
165
,
sunlet
4
)-free
(3K
1
,
2P
3
)-free
(3K
1
,
3K
2
)-free
(3K
1
,
C
6
)-free
(3K
1
,
E
)-free
(3K
1
,
H
)-free
(3K
1
,
K
1,5
)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
2
∪ P
4
)-free
(3K
1
,
P
6
)-free
(3K
1
,
T
2
,
X
2
,
X
3
,anti-hole)-free
(3K
1
,
X
172
)-free
(3K
1
,
XC
12
)-free
(3K
1
,co-cross)-free
3K
1
-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
6
,P
7
,X
164
,X
165
,odd-cycle,sunlet
4
)-free
(3K
2
,
P
,co-gem,house)-free
(3K
2
,co-paw,odd anti-hole)-free
(3K
3
,C
n+4
)-free
(3P
3
,C
n+4
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,
A
)-free
(4,0)-colorable
(4-fan,C
n+4
,K
5
- e,S
3
,X
100
,X
101
,X
102
,
H
,
K
3
∪ 2K
1
)-free
(4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
4-leaf power
(4K
1
,C
7
,S
3
,X
175
,X
176
,X
42
,
X
36
,claw,co-antenna,net,odd anti-hole)-free
(4K
1
,C
7
,X
195
,X
196
,X
38
,X
39
,
W
5
,
X
194
,
X
86
,
X
88
,
X
89
,
X
90
,house)-free
(4K
1
,C
7
,X
38
,X
39
,
K
3,3
∪ K
1
,
W
4
∪ K
1
,
W
5
,
X
86
,
X
87
,
X
88
,
X
89
,
X
90
,butterfly ∪ K
1
,diamond)-free
(4K
1
,
C
n+4
)-free
(4K
1
,co-claw,co-diamond)-free
(4K
1
,gem)-free
(4K
1
,house)-free
(4K
1
,net)-free
(4K
1
,odd anti-hole,odd-hole)-free
4K
1
-free
5-leaf power
(6,1)-chordal ∩ bipartite
6K
1
-free
7K
1
-free
(A,E,S
3
,X
1
,domino,hole,house,net,rising sun)-free
(A,T
2
,odd-cycle)-free
(A,
3P
3
,
C
n+4
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,house)-free
AT-free
AT-free ∩ claw-free
Apollonian network
B
0
-VPG ∩ chordal
B
0
-VPG ∩ strongly chordal
(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
)-free ∩ maximum degree 3 ∩ planar
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free ∩ planar
C
4
-free ∩ induced-hereditary pseudo-modular
(C
5
,C
6
∪ K
1
,C
7
,K
3,3
∪ K
1
,K
3,3
-e ∪ K
1
,
K
5
- e
,domino ∪ K
1
,triangle)-free
(C
5
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P
5
,gem)-free
(C
5
,bull,co-gem,gem)-free
(C
5
,co-gem,gem)-free
(C
5
,co-gem,house)-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
,K
4
)-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
,S
3
)-free
(C
n+4
,T
2
,XF
2
n+1
)-free
(C
n+4
,T
2
,net)-free
(C
n+4
,X
59
,longhorn)-free
(C
n+4
,XF
1
2n+3
,XF
6
2n+2
,
X
34
,
X
36
,co-XF
2
n+1
,co-XF
3
n
)-free
(C
n+4
,claw,net)-free
(C
n+4
,claw)-free
(C
n+4
,odd-sun)-free
(C
n+4
,sun)-free
C
n+4
-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,X
37
,X
38
,X
39
,X
40
,X
41
,XF
2
n+1
,XF
3
n
,XF
4
n
)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,XF
2
n+1
,XF
3
n
,XF
4
n
,anti-hole,co-XF
1
2n+3
,co-XF
5
2n+3
,co-XF
6
2n+2
)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,XF
2
n+1
,XF
3
n
,XF
4
n
,co-XF
1
2n+3
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd anti-hole)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
36
,XF
1
2n+3
,XF
2
n+1
,XF
3
n
,XF
4
n
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
36
,co-XF
1
2n+3
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd anti-hole)-free
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
36
,XF
1
2n+3
,XF
2
n+1
,XF
3
n
,XF
4
n
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
36
,co-XF
1
2n+3
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,co-XF
5
2n+3
,co-XF
6
2n+2
,odd-hole)-free
(C
n+6
,X
37
,claw,co-antenna,net,sun)-free
(C
n+6
,odd-cycle)-free
Dilworth 2
(E,odd-cycle)-free
E-free ∩ bipartite
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
Halin
Helly chordal
Helly chordal ∩ clique-chordal
Helly circle
Helly circular arc
Helly circular arc ∩ (
C
7
,odd-hole)-free
Helly circular arc ∩ concave-round
Helly circular arc ∩ perfect
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
H
n,q
grid
(K
1,4
,odd-cycle)-free
(K
1,4
,odd-cycle)-free ∩ planar
(K
2
∪ K
3
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2
∪ claw,triangle)-free
(K
2,3
,K
4
)-minor-free
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-free
(K
3,3,3
,
C
n+4
)-free
(K
3,3
,K
3,3
+e,
2P
3
,
C
n+4
)-free
(K
3,3
,
C
n+4
)-free
K
4
-minor-free
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
N
*
(P,P
5
,
3K
2
,gem)-free
(P,P
5
,co-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
-indifference
(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,odd anti-hole)-free
(P
5
,bull)-free
(P
5
,gem)-free
(P
6
,triangle)-free
PI
PI
*
(S
3
,
C
n+4
,
S
3
∪ K
1
,co-claw)-free
(S
3
,
C
n+4
,
T
2
)-free
(S
3
,
C
n+4
,co-claw,net)-free
(S
3
,
C
n+4
,co-claw)-free
(S
3
,
C
n+4
,net)-free
(S
3
,net)-free ∩ chordal
(S
3
,net)-free ∩ split
S
3
-free ∩ chordal
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(T
2
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
X-conformal ∩ bipartite ∩ hereditary X-chordal
(X
103
,
C
n+4
,
S
3
∪ K
1
,
net ∪ K
1
,co-claw,co-eiffeltower)-free
(X
172
,triangle)-free
(X
177
,odd-cycle)-free
(X
34
,X
36
,XF
2
n+1
,XF
3
n
,
C
n+4
,co-XF
1
2n+3
,co-XF
6
2n+2
)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
(XC
12
,triangle)-free
(XC
12
,triangle)-free ∩ planar
(XC
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(
2C
4
,
3K
2
,
C
6
,
E
,
P
2
∪ P
4
,
P
6
,
X
25
,
X
26
,
X
27
,
X
28
,
X
29
,odd anti-cycle)-free
(
3K
2
,
C
6
,
P
7
,
X
164
,
X
165
,
sunlet
4
,odd anti-cycle)-free
(
A
,
T
2
,odd anti-cycle)-free
(
C
n+3
∪ K
1
,co-diamond,co-paw)-free
(
C
n+4
,
H
)-free
(
C
n+4
,
T
2
,
X
31
,co-XF
2
n+1
,co-XF
3
n
)-free
(
C
n+4
,
T
2
,co-XF
2
n+1
)-free
(
C
n+4
,
X
59
,co-longhorn)-free
(
C
n+4
,bull,co-dart,co-gem)-free
(
C
n+4
,co-claw,co-gem)-free
(
C
n+4
,co-claw)-free
(
C
n+4
,co-dart,co-gem)-free
(
C
n+4
,co-diamond)-free
(
C
n+4
,co-gem)-free
(
C
n+4
,co-sun)-free
(
C
n+4
,net)-free
(
C
n+4
,odd co-sun)-free
C
n+4
-free
(
C
n+6
,odd anti-cycle)-free
(
E
,odd anti-cycle)-free
(
K
1,4
,co-paw)-free
(
K
1,4
,odd anti-cycle)-free
(
P
7
,
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
P
7
,
star
1,2,3
,odd anti-cycle)-free
(
P
7
,odd anti-cycle)-free
(
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,even anti-hole,odd anti-cycle)-free
(
T
2
,co-cycle)-free
(
T
3
,
X
81
,co-cycle)-free
(
T
3
,co-cycle)-free
W
2n+3
-free
(
X
177
,odd anti-cycle)-free
(
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
,co-cycle)-free
XC
12
-free
XC
13
-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
(
star
1,2,3
,
sunlet
4
,odd anti-cycle)-free
(
star
1,2,3
,odd anti-cycle)-free
τ
k
-perfect for all k >= 2
absolutely perfect
almost CIS
almost tree (1)
alternately orientable ∩ co-comparability
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,odd anti-cycle)-free
b-perfect ∩ chordal
balanced ∩ chordal
basic 4-leaf power
biconvex
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ girth >=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ probe interval
bipartite ∩ tolerance
bipartite ∩ weakly chordal
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
cactus
chordal
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ dominating pair
chordal ∩ domination perfect
chordal ∩ dually chordal
chordal ∩ hamiltonian
chordal ∩ hamiltonian ∩ planar
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ maximal planar
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ planar
chordal ∩ proper circular arc
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal bipartite
circle
circle ∩ diamond-free
circle graph with equator
circle-n-gon, fixed n
circle-trapezoid
circular arc
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular interval
circular strip
(claw ∪ 3K
1
,odd-cycle)-free
claw-free ∩ normal Helly circular arc
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
cliquewidth 3
cliquewidth 4
co-2-subdivision
co-β-perfect
co-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold ∩ split
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-comparability
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 2
co-comparability graphs of posets of interval dimension d
co-cycle-free
(co-diamond,even anti-cycle)-free
(co-diamond,house)-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-leaf power
(co-paw,odd anti-hole)-free
co-paw-free
co-planar
co-probe cograph
co-proper interval bigraph
co-strongly chordal
co-threshold tolerance
comparability ∩ split
comparability graphs of dimension 2 posets
comparability graphs of posets of interval dimension 2, height 2
comparability graphs of semiorders
concave-round
containment graph of intervals
convex
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
d-trapezoid
directed path
doubly chordal
even anti-cycle-free
grid graph ∩ maximum degree 3
hamiltonian ∩ split
hereditary Helly
hereditary disk-Helly
hereditary dually chordal
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
intersection graphs of parallelograms (squares)
interval bigraph
interval containment bigraph
k-outerplanar
k-path graph, fixed k
k-polygon
k-starlike
k-tree, fixed k
leaf power
leaf power ∩ min leaf power
leaf power ∪ min leaf power
maximal outerplanar
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
min leaf power
mock threshold ∩ split
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
outerplanar
overlap
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 4-tree
partial k-tree, fixed k
path orderable
permutation
planar of maximum degree 3
power-chordal
probe P
4
-reducible
probe P
4
-sparse
probe bipartite chain
probe bipartite distance-hereditary
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe distance-hereditary
probe proper interval
probe ptolemaic
probe threshold
probe trivially perfect
probe unit interval
proper Helly circular arc
proper circular arc
proper tolerance
pseudo-split
rigid circuit
rooted directed path
series-parallel
split
split ∩ strongly chordal
split ∩ superperfect
square of tree
strong asteroid free
strong tree-cograph
strongly chordal
threshold signed
threshold tolerance
tolerance ∩ triangle-free
trapezoid
tree-cograph
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
triangulated
undirected path
unicyclic
unit Helly circle
unit Helly circular arc
unit circular arc
unit tolerance
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
(0,2)-colorable
(0,3)-colorable
(1,2)-colorable
(1,2)-split
1-string
(2,2)-colorable
(2,2)-interval
2-DIR
2-SEG
2-circular arc
2-circular track
2-connected
2-edge-connected
2-interval
2-split
2-split ∩ perfect
2-subdivision
2-subdivision ∩ planar
2-track
(2K
3
+ e,
X
98
,house)-free
(2K
3
+ e,
X
99
,house)-free
(2K
3
+ e,house)-free
(2K
3
,2K
3
+ e,
A
,
H
,
X
45
,
XZ
5
,co-domino)-free
(2K
3
,X
42
,
A
,
H
,
X
45
,
X
46
,
X
47
,
X
48
,
X
49
,
X
50
,
X
51
,
X
52
,
X
53
,
X
54
,
X
55
,
X
56
,
X
57
)-free
(2K
3
,house)-free
(2K
4
,house)-free
3-DIR
3-DIR contact
3-circular track
3-interval
3-mino
3-track
4-colorable
(4-fan,K
1,4
,W
4
,W
5
,
A ∪ K
1
,
co-fork ∪ K
1
,
gem ∪ K
1
,
net ∪ K
1
)-free
4-regular
4-regular ∩ hamiltonian
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(5,2)
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
5-colorable
(5-pan,T
2
,X
172
)-free
5-regular
5-regular ∩ hamiltonian
6-colorable
(A,H,K
3,3
,K
3,3
-e,X
45
,XZ
5
,domino)-free
(A,H,K
3,3
,X
45
,X
46
,X
47
,X
48
,X
49
,X
50
,X
51
,X
52
,X
53
,X
54
,X
55
,X
56
,X
57
,
X
42
)-free
(A,H,K
3,3
,X
45
,triangle)-free
B
0
-VPG
B
0
-VPG ∩ bipartite
B
0
-VPG ∩ triangle-free
B
1
-CPG
B
1
-CPG ∩ triangle-free
B
1
-VCPG
B
1
-VPG
B
2
-VPG
B
3
-VPG
(BW
3
,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
Berge
Berge ∩ bull-free
Berge ∩ claw-free
B
k
-VPG
Bouchet
(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
,K
4
,diamond)-free ∩ planar
(C
4
,C
5
)-free
(C
4
,S
3
)-free
(C
4
,
A
,
H
)-free
(C
4
,co-claw)-free
(C
4
,diamond)-free
(C
4
,triangle)-free
(C
4
,triangle)-free ∩ planar
C
4
-free
(C
5
,C
6
,X
164
,X
165
,sunlet
4
,triangle)-free
(C
5
,P,
P
,bull,co-fork,gem,house)-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free
(C
5
,house)-free
C
5
-free
(C
6
,
C
6
)-free
(C
6
,house)-free
(C
6
,triangle)-free
C
6
-free
(C
7
,odd anti-hole)-free
CONV
CPG
(E,P)-free
E-free
EPT
Gallai
Gallai-perfect
(H,triangle)-free
Helly 2-acyclic subtree
(K
1,4
,diamond)-free
K
1,4
-free
(K
1,5
,triangle)-free
(K
2
∪ K
3
,X
11
,X
127
,X
128
,X
129
,X
131
,X
133
,X
135
,X
136
,X
137
,X
138
,X
139
,X
140
,X
141
,X
142
,X
143
,X
144
,X
145
,X
146
,X
147
,X
148
,X
149
,X
150
,X
151
,X
30
,X
35
,X
46
,XF
1
2n+3
,XF
6
2n+3
,
2P
3
,
3K
2
,
C
4
∪ P
2
,
C
6
,
P
6
,
X
130
,
X
132
,
X
134
,
X
152
,
X
153
,
X
154
,
X
155
,
X
156
,
X
157
,
X
158
,
X
18
,
X
84
,antenna,co-domino,co-fish,eiffeltower,longhorn,odd-hole)-free
(K
2
∪ K
3
,
P
,anti-hole)-free
(K
2
∪ K
3
,
P
,house)-free
(K
2
∪ K
3
,house)-free
K
2
∪ K
3
-free
K
2
∪ claw-free
(K
2,3
,X
37
,X
38
,diamond,domino,house,twin-C
5
)-free
(K
2,3
,diamond)-free
K
2,3
-free
(K
3
∪ 2K
1
,
K
3
∪ 2K
1
,bull,co-cricket,co-dart,cricket,dart)-free
(K
3
∪ P
3
,
C
6
,
P
,
P
7
,
X
37
,
X
41
)-free
(K
3,3
,K
5
)-minor-free
(K
4
,S
3
,X
36
,
C
7
,
X
175
,
X
176
,
X
42
,antenna,co-claw,net,odd-hole)-free
(K
4
,S
3
)-free
(K
4
,odd anti-hole,odd-hole)-free
K
4
-free
K
4
-free ∩ perfect
(K
5
- 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
6
-free
K
7
-free
Meyniel
(P,T
2
)-free
(P,co-fork)-free
(P,star
1,2,3
)-free
(P,star
1,2,4
)-free
(P,star
1,2,5
)-free
P-free
P
4
-bipartite
P
4
-brittle
P
4
-comparability
PURE-2-DIR
PURE-3-DIR
PURE-k-DIR
(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
,co-claw,net)-free
(S
3
,co-claw)-free
(S
3
,net)-free
(S
3
,net)-free ∩ sun-free
S
3
-free
SEG
VPG
W
2n+3
-free
(W
4
,W
5
,butterfly)-free
(W
4
,claw,gem,odd-hole)-free
(W
4
,claw,gem)-free
(W
4
,claw)-free
(W
4
,gem)-free
(W
4
,gem)-free ∩ short-chorded
W
n+4
-free
(X
12
,X
5
,X
95
,X
96
,X
97
,
X
12
,
X
5
,
X
95
,
X
96
,
X
97
,
claw ∪ triangle
,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X
30
,XZ
1
,XZ
4
,longhorn)-free
(X
38
,gem,house)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free
(X
79
,X
80
)-free
XC
10
-free
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
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
,odd-hole)-free
(G)-perfect
3
-perfect
2P
3
-free
(
3K
2
,odd-hole,paw)-free
(
5-pan
,
T
2
,
X
172
)-free
(
A
,
P
6
,co-domino)-free
BW
3
-free
C
6
-free
(
C
7
,odd-hole)-free
(
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
35
,
X
36
,
X
37
,
X
38
,
X
39
,
X
40
,
X
41
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
)-free
C
n+6
-free
C
n+7
-free
(
E
,
P
)-free
E
-free
(
K
1,4
,
P
,co-fork,house)-free
(
K
1,4
,house)-free
K
1,4
-free
K
2
∪ claw
-free
(
P
,
P
7
)-free
(
P
,
P
8
)-free
(
P
,
T
2
)-free
(
P
,
star
1,2,3
)-free
(
P
,co-star
1,2,4
)-free
(
P
,co-star
1,2,5
)-free
(
P
,house)-free
P
-free
P
2
∪ P
4
-free
(
P
6
,
X
30
,
X
8
)-free
(
P
6
,co-claw)-free
P
6
-free
P
7
-free
(
X
30
,
XZ
1
,
XZ
4
,co-longhorn)-free
(
X
79
,
X
80
)-free
(
X
82
,
X
83
,house)-free
(
X
91
,co-claw)-free
(n+4)-pan
-free
odd-cycle ∪ K
1
-free
absorbantly perfect
all-4-simplicial
almost claw-free
alternately colourable
alternately orientable
alternation
(anti-hole,bull,odd-hole)-free
(anti-hole,odd-hole)-free
anti-hole-free
apex
balanced
balanced 2-interval
balanced ∩ line
balanced ∩ paw-free
basic perfect
biclique-Helly
bip
*
bipartite
bipartite ∩ boxicity 2
bipartite ∩ grid intersection
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ planar
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
book thickness 2
boxicity 2
building-free
building-free ∩ even-signable
(bull,co-fork)-free
(bull,house,odd-hole)-free
(bull,house)-free
(bull,odd anti-hole,odd-hole)-free
bull-free
bull-free ∩ perfect
(butterfly,gem)-free
caterpillar arboricity <= 2
circular perfect
(claw,diamond,odd-hole)-free
(claw,diamond)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ perfect
clique graphs
clique separable
clique-Helly
clique-perfect
clique-perfect ∩ triangle-free
(co-butterfly,co-claw)-free
co-circular perfect
(co-claw,house)-free
(co-claw,odd anti-hole,odd-hole)-free
(co-claw,odd anti-hole)-free
(co-claw,odd-hole)-free
co-claw-free
co-comparability ∪ comparability
(co-cricket,house)-free
co-domino-free
(co-fork,house)-free
co-fork-free
co-interval filament
co-interval mixed
co-quasi-line
co-sun-free
co-unipolar
co-unipolar ∪ unipolar
coin
comparability
containment graphs
cycle-bicolorable
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
disk
disk contact
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
domino
(domino,gem,house)-free
domino-free
even anti-hole-free
even-signable
fork-free
gem-free
generalized split
genus 0
genus 1
girth >=9
grid intersection
gridline
hamiltonian
hamiltonian ∩ planar
hereditary biclique-Helly
hereditary clique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
house-free
i-triangulated
k-DIR
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 planar cubic bipartite graphs
line graphs of triangle-free graphs
linear domino
locally bipartite
locally chordal
locally perfect
locally split
maximal clique irreducible
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
monopolar
(n+4)-pan-free
nearly bipartite
neighbourhood chordal
neighbourhood perfect
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
net-free
normal
(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 ∩ planar
odd-hole-free ∩ pretty
odd-sun-free
open-neighbourhood-Helly
(p,q<=2)-colorable
p-connected
parity
partial bar visibility
partial rectangle visibility
paw-free
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect cochromatic
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
planar
planar ∩ triangle-free
planar of maximum degree 4
polar
preperfect
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe Gallai
probe Meyniel
probe chordal
probe comparability
probe diamond-free
probe split
quasi-Meyniel
quasi-line
quasi-parity
rectangle intersection
rectangle visibility
short-chorded
skeletal
slender
slim
split-neighbourhood
star convex
strict quasi-parity
strictly clique irreducible
string
strong domination perfect
strongly 3-colorable
strongly circular perfect
strongly even-signable
strongly perfect
subhamiltonian
sun-free
superperfect
thickness <= 2
toroidal
totally unimodular
tree convex
triangle contact
triangle-free
tripartite
unimodular
unit 2-circular arc
unit 2-interval
unit 3-interval
upper domination perfect
upper irredundance perfect
very strongly perfect
weak bar visibility
weak bisplit
weak rectangle visibility
weakly geodetic
back to top
coNP-complete
back to top
Open
back to top
Unknown to ISGCI
(0,2)-graph
(0,2)-graph ∩ bipartite
(1,2)-polar
1-bounded tripartite
2-connected ∩ (P
6
,claw)-free
2-connected ∩ linearly convex triangular grid graph
2-strongly regular
2-strongly regular ∩ planar
2-thin
2-threshold
(2K
3
+ e,5-pan,A,C
6
,E,K
3,3
-e,P
6
,R,X
166
,X
167
,X
169
,X
170
,X
171
,X
172
,X
18
,X
37
,X
45
,X
5
,X
58
,X
84
,X
95
,X
98
,
5-pan
,
A
,
C
6
,
E
,
P
6
,
R
,
X
166
,
X
167
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
37
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
98
,antenna,co-antenna,co-domino,co-fish,co-twin-C
5
,co-twin-house,domino,fish,twin-C
5
,twin-house)-free
(2K
3
+ e,A,C
5
,C
6
,E,H,K
3,3
-e,R,X
168
,X
171
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,
A
,
C
6
,
E
,
H
,
R
,
X
168
,
X
171
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K
3
+ e,A,C
5
,C
6
,E,K
3,3
-e,P
6
,R,X
166
,X
167
,X
169
,X
170
,X
171
,X
172
,X
18
,X
45
,X
5
,X
58
,X
84
,X
95
,X
98
,
A
,
C
6
,
E
,
P
6
,
R
,
X
166
,
X
167
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
98
,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K
3
+ e,C
5
,C
6
,P
6
,X
5
,
2P
4
,
A
,
C
6
,
C
7
,
E
,
P
7
,
R
,
X
1
,
X
103
,
X
5
,
X
58
,
X
84
,
X
98
,antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet
4
)-free
(2K
3
,2K
3
+ e,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,W
4
,X
84
,X
95
,
A
,
C
6
,
P
6
,
X
5
,
X
98
,butterfly,co-domino,co-fish,fish)-free
(2K
3
,2P
3
,C
5
,C
6
,C
7
,K
2,3
,K
3
∪ P
3
,X
84
,
3K
2
,
C
4
∪ P
2
,
C
6
,
P
2
∪ P
4
,
P
6
,
X
18
,
X
5
,co-antenna,co-domino,co-fish)-free
(2P
3
,3K
2
,C
4
∪ P
2
,C
6
,K
2,3
,P
6
,X
130
,X
132
,X
134
,X
152
,X
153
,X
154
,X
155
,X
156
,X
157
,X
158
,X
18
,X
84
,
X
11
,
X
127
,
X
128
,
X
129
,
X
131
,
X
133
,
X
135
,
X
136
,
X
137
,
X
138
,
X
139
,
X
140
,
X
141
,
X
142
,
X
143
,
X
144
,
X
145
,
X
146
,
X
147
,
X
148
,
X
149
,
X
150
,
X
151
,
X
30
,
X
35
,
X
46
,co-XF
1
2n+3
,co-XF
6
2n+3
,co-antenna,co-eiffeltower,co-longhorn,domino,fish,odd anti-hole)-free
(2P
3
,C
4
,C
6
)-free
(2P
3
,triangle)-free
2P
3
-free
(2P
4
,A,C
5
,C
6
,C
7
,E,K
3,3
-e,P
7
,R,X
1
,X
103
,X
5
,X
58
,X
84
,X
98
,
C
6
,
P
6
,
X
5
,
sunlet
4
,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
3-Helly
(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
,triangle)-free
(3P
3
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,X
184
,X
185
,X
186
,X
187
,X
188
,X
189
,X
190
,X
191
,X
192
,X
193
,
5-pan
,
A
,
P
6
,co-twin-C
5
)-free
3d grid
(5,2)-chordal
(5-pan,A,P
6
,X
186
,
3P
3
,
P
3
∪ P
4
,
X
102
,
X
180
,
X
181
,
X
182
,
X
183
,
X
184
,
X
185
,
X
187
,
X
188
,
X
189
,
X
190
,
X
191
,
X
192
,
X
193
,house,twin-C
5
)-free
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,1)-chordal
(6,1)-even-chordal
(6,2)-chordal
(6,3)
(6-fan,C
4
∪ P
2
,C
5
,C
6
∪ K
1
,C
7
,K
2
∪ K
3
,K
2,3
,P
2
∪ P
4
,W
4
∪ K
1
,W
6
,X
132
,X
169
,X
176
,X
18
,X
197
,X
198
,X
199
,X
200
,X
201
,X
202
,X
35
,X
84
,
C
4
∪ P
2
,
C
6
∪ K
1
,
C
7
,
P
2
∪ P
4
,
W
4
∪ K
1
,
W
6
,
X
132
,
X
169
,
X
176
,
X
18
,
X
197
,
X
198
,
X
199
,
X
200
,
X
201
,
X
35
,
X
84
,
butterfly ∪ K
1
,butterfly ∪ K
1
,co-6-fan,co-fish,fish)-free
(7,5)
(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,T
2
,X
18
,X
45
,domino,triangle)-free
(A,P
6
,clique wheel,domino,hole,house)-free
(A,P
6
,domino)-free
B
0
-CPG
(BW
3
,C
5
,K
3,4
,K
3,4
-e,T
2
,X
18
,X
92
,X
93
,triangle)-free
BW
3
-free ∩ modular
Birkhoff
(C
4
∪ P
2
,C
5
,C
6
,K
2
∪ K
3
,K
2,3
,P
6
,W
4
,X
18
,X
5
,X
84
,
C
4
∪ P
2
,
C
6
,
P
6
,
W
4
,
X
18
,
X
5
,
X
84
,antenna,co-antenna,co-domino,co-fish,domino,fish)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,XC
11
,claw,diamond)-free
(C
4
,C
5
,T
2
)-free
(C
4
,C
5
)-free ∩ Helly
(C
4
,C
5
)-free ∩ cop-win
(C
4
,C
6
,odd-cycle)-free
(C
4
,K
4
,claw,diamond)-free
(C
4
,P
5
)-free
(C
4
,P
6
)-free
(C
4
,X
91
,claw)-free
(C
4
,claw,diamond)-free
(C
4
,odd-hole)-free
C
4
-free ∩ C
6
-free ∩ bipartite
C
4
-free ∩ odd-signable
C
4
-free ∩ perfect
(C
5
,C
6
,C
7
,C
8
,P
8
,X
19
,X
20
,X
21
,X
22
,gem,house)-free
(C
5
,C
6
,P
6
,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
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-free
(C
5
,P,P
5
,
P
,house)-free
(C
5
,P,P
5
,house)-free
(C
5
,P,co-fork,fork,gem,house)-free
(C
5
,P
2
∪ P
3
,house)-free
(C
5
,P
5
,
A
,
C
6
,
P
6
,co-domino)-free
(C
5
,P
5
,
C
6
,
C
7
,
C
8
,
P
8
,
X
19
,
X
20
,
X
21
,
X
22
,co-gem)-free
(C
5
,P
5
,
P
,co-fork,co-gem,fork)-free
(C
5
,P
5
,
P
,house)-free
(C
5
,P
5
,
P
2
∪ P
3
)-free
(C
5
,P
5
,co-fish,fish,house)-free
(C
5
,P
5
,house)-free
(C
5
,P
5
)-free
(C
5
,P
6
,
P
6
)-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free ∩ co-line
(C
6
,C
8
,T
2
,X
3
,
BW
3
,
W
5
,
W
7
,
X
103
,
X
105
,
X
106
,
X
107
,
X
108
,
X
109
,
X
110
,
X
111
,
X
112
,
X
113
,
X
114
,
X
115
,
X
116
,
X
117
,
X
118
,
X
119
,
X
120
,
X
121
,
X
122
,
X
123
,
X
124
,
X
125
,
X
126
,
X
53
,
X
88
,co-X
104
)-free
(C
6
,K
2
∪ K
3
,X
103
,X
37
,X
88
,X
90
,
C
n+4
∪ K
1
,
T
2
,
net ∪ K
1
,co-diamond,co-domino,co-eiffeltower,co-twin-C
5
)-free
(C
6
,K
2
∪ K
3
,X
37
,X
90
,
C
n+4
∪ K
1
,
T
2
,
W
n+4
,
X
31
,co-XF
2
n+1
,co-XF
3
n
,co-domino,co-twin-C
5
)-free
(C
6
,K
3,3
+e,P,P
7
,X
37
,X
41
)-free
(C
6
,P
6
,
P
6
,
X
10
,
X
11
,
X
12
,
X
13
,
X
14
,
X
15
,
X
5
,
X
6
,
X
7
,
X
8
,
X
9
,anti-hole,co-antenna)-free
(C
6
,S
3
,
C
n+4
∪ K
1
,
W
4
,
W
5
,co-claw,net)-free
(C
6
,
C
6
)-free murky
C
6
-free ∩ modular
CIS
(C
n+3
∪ K
1
,diamond,paw)-free
C
n+6
-free
C
n+7
-free
D
Delaunay
Deza
Dilworth 3
Dilworth 4
(E,triangle)-free
E-free ∩ planar
F
n
grid
Gabriel
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamilton-connected
Hamiltonian hereditary
Hamming
Helly
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly subtree
Hilbertian
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-free
(K
1,4
,paw)-free
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
(K
2
∪ K
3
,P
5
,
X
37
,
X
38
,co-diamond,co-domino,co-twin-C
5
)-free
(K
2
∪ K
3
,co-diamond)-free
(K
2,3
,P,P
5
)-free
(K
2,3
,P,hole)-free
(K
2,3
,P
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
,P
5
)-free
(K
3,3
-e,P
5
,X
98
)-free
(K
3,3
-e,P
5
,X
99
)-free
(K
3,3
-e,P
5
)-free
(K
4,4
,P
5
)-free
(K
4
,P
5
,W
5
,X
194
,X
86
,X
88
,X
89
,X
90
,
C
7
,
X
195
,
X
196
,
X
38
,
X
39
)-free
(K
4
,P
5
)-free
(K
4
,claw,diamond)-free
(K
4
,co-gem)-free
(K
4
,odd anti-hole,odd-hole)-free ∩ dually chordal
K
4
-free ∩ dually chordal ∩ perfect
Laman
Laman ∩ planar
Matula perfect
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
Mycielski
N
*
-perfect
(P,P
5
)-free
(P,P
7
)-free
(P,P
8
)-free
(P
2
∪ P
3
,house)-free
(P
2
∪ P
4
,triangle)-free
P
2
∪ P
4
-free
P
4
-laden
P
4
-simplicial
(P
5
,S
3
,
A
,
E
,
X
1
,anti-hole,co-domino,co-rising sun,net)-free
(P
5
,X
82
,X
83
)-free
(P
5
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,anti-hole,co-bicycle,co-domino)-free
(P
5
,anti-hole,co-domino,co-sun)-free
(P
5
,anti-hole,co-domino)-free
(P
5
,anti-hole,co-gem)-free
(P
5
,anti-hole)-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 ∩ tripartite
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
6
-free ∩ tripartite
(P
7
,odd-cycle)-free
P
7
-free
P
7
-free ∩ bipartite
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
,claw,net)-free
Urquhart
V-perfect
Welsh-Powell opposition
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-star-chordal
(X
37
,diamond,even-cycle)-free
(X
79
,X
80
)-free ∩ modular
(X
91
,claw)-free
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(XC
11
,claw,diamond)-free
(XF
1
2n+3
,XF
5
2n+3
,XF
6
2n+2
,
C
n+6
,
T
2
,
X
2
,
X
3
,
X
30
,
X
31
,
X
32
,
X
33
,
X
34
,
X
35
,
X
36
,co-XF
2
n+1
,co-XF
3
n
,co-XF
4
n
,hole)-free
β-perfect
(
K
1,4
,co-diamond)-free
(
P
,fork)-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
XC
10
-free
absolute bipartite retract
absolute reflexive retract
almost median
almost-split
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
b-perfect
balanced ∩ co-line
bar visibility
biclique separable
bigeodetic
binary Hamming
bipartable
bipartite ∩ quasi-median
bipartite ∩ unit grid intersection
bipolarizable
bithreshold
bitolerance
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
bridged
bridged ∩ clique-Helly
brittle
building-free ∩ odd-signable
(bull,fork)-free
(bull,hole,odd anti-hole)-free
(butterfly,claw)-free
charming
chordal-perfect
circle-polygon
circular convex bipartite
circular permutation
circular trapezoid
(claw,net)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ upper domination perfect
claw-free ∩ well covered
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-Helly ∩ dismantlable ∩ reflexive
clique-chordal
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P
4
-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-biclique separable
co-bithreshold
co-bounded tolerance
co-building-free
(co-butterfly,co-gem)-free
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-forest-perfect
(co-fork,hole)-free
co-gem-free
co-hereditary clique-Helly
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
co-perfectly orderable
co-tolerance
co-trapezoid
cograph contraction
comparability ∩ weakly chordal
comparability graphs of dimension 3 posets
comparability graphs of dimension 4 posets
comparability graphs of dimension d posets
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension 2, height 3
comparability graphs of posets of interval dimension d
complete Hamming
containment graph of circles
containment graphs of circular arcs
convex-round
cop-win
(cross,triangle)-free
cubical
diametral path
(diamond,even-cycle)-free
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
dominating pair
domination
double split
doubled
dually chordal
dually chordal ∩ tripartite
edge regular
equimatchable
even-cycle-free
even-hole-free
even-hole-free ∩ probe chordal
extended P
4
-laden
forest-perfect
(fork,house)-free
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
generalized strongly chordal
generically minimally rigid
geodetic
good
graceful
grid
grid graph
half-disk Helly
harmonious
hereditary Matula perfect
hereditary N
*
-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary clique-Helly ∩ self-clique
hereditary dismantlable
hereditary homogeneously orderable
hereditary median
hereditary modular
hereditary sat
hereditary weakly modular
(hole,odd anti-hole)-free
hole-free
hole-free ∩ planar
homogeneously orderable
homothetic triangle contact
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
hypercube
induced-hereditary pseudo-modular
interval enumerable
interval filament
interval regular
interval regular of diameter 2
irredundance perfect
irredundance perfect with ir(G)=2
irredundance perfect with ir(G)<= 4
isometric subgraph of a hypercube
isometric-HH-free
isometric-hereditary pseudo-modular
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
line ∩ mock threshold
line ∩ well covered
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
max-tolerance
maxibrittle
maximal planar
median
median ∩ planar
middle
mock threshold
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
nK
2
-free, fixed n
nP
3
-free, fixed n
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
odd-signable
odd-signable ∩ triangle-free
opposition
outer-string
(p,q)-colorable
(p,q)-split
p-tree
pairwise compatibility
parallelepiped
partial 3d grid
partial cube
partial grid
partitionable
perfect connected-dominant
planar ∩ strongly regular
polyhedral
premedian
probe AT-free
probe HHDS-free
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-bipartite
probe co-comparability
probe interval
probe interval bigraph
probe permutation
probe strongly chordal
pseudo-median
pseudo-median ∩ triangle-free
pseudo-modular
pseudo-modular ∩ triangle-free
(q,t)
quasi-brittle
quasi-median
quasitriangulated
rectagraph
reflexive
relative neighbourhood graph
self-clique
self-complementary
semi-median
semi-square intersection
semiperfectly orderable
slightly triangulated
solid grid graph
solid triangular grid graph
spider graph
split-perfect
strict 2-threshold
strict B
1
-VCPG
strongly odd-signable
strongly orderable
strongly regular
subtree filament
subtree overlap
sun-free ∩ weakly chordal
superbrittle
tolerance
trapezoepiped
tree-perfect
triangular grid graph
unbreakable
unigraph
unipolar
unit 2-circular track
unit 2-track
unit 3-circular track
unit 3-track
unit bar visibility
unit disk
unit grid intersection
visibility
walk regular
weak bipolarizable
weak dominating pair
weakly chordal
weakly median
weakly modular
well covered
well-dominated
wing-triangulated
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