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This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown
Problem: Clique
Definition:
Input: A graph
G
in this class and an integer
k
.
Output: True iff
G
contains a set
S
of pairwise adjacent vertices, with |
S
| >=
k
.
Linear
(0,2)-colorable
(0,2)-colorable ∩ chordal
(0,2)-graph ∩ bipartite
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar ∩ chordal
1-bounded bipartite
(2,0)-colorable ∩ chordal
2-bounded bipartite
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
,A,C
5
,
2P
3
,
X
170
,house)-free
(2K
2
,C
4
,C
5
,H,S
3
,X
160
,
X
159
,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,X
159
,X
160
,
H
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,S
3
,claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-claw,net)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,co-rising sun,net)-free
(2K
2
,C
4
,C
5
,S
3
,net,rising sun)-free
(2K
2
,C
4
,C
5
,S
3
,net)-free
(2K
2
,C
4
,C
5
,claw,diamond)-free
(2K
2
,C
4
,C
5
,co-claw,co-diamond)-free
(2K
2
,C
4
,C
5
,co-sun)-free
(2K
2
,C
4
,C
5
,sun)-free
(2K
2
,C
4
,C
5
)-free
(2K
2
,C
4
,P
4
,triangle)-free
(2K
2
,C
4
,P
4
)-free
(2K
2
,C
5
,S
3
,X
159
,X
160
,X
161
,X
162
,X
46
,X
70
,
2P
3
,
3K
2
,
H
,
P
2
∪ P
4
,
X
1
,co-rising sun,house,net)-free
(2K
2
,C
5
,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
+ 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
,2P
3
,C
4
,K
3
∪ P
3
,P
4
)-free
(2K
3
,2P
3
,C
n+4
,K
3
∪ P
3
)-free
(2K
3
,C
n+4
)-free
(2P
3
,3K
2
,C
4
,C
5
,H,P
2
∪ P
4
,P
5
,S
3
,X
1
,X
160
,
X
159
,
X
161
,
X
162
,
X
46
,
X
70
,net,rising sun)-free
(2P
3
,C
4
,C
5
,P
5
,X
170
,
A
)-free
(2P
3
,C
4
,P
4
)-free
(2P
3
,P
4
)-free
3-leaf power
3-tree
3-tree ∩ planar
(3K
1
,C
4
,C
5
)-free
(3K
1
,C
4
,
P
3
)-free
(3K
1
,C
5
,
C
6
,
P
6
)-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
(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
(3P
3
,C
n+4
,P
3
∪ P
4
,P
5
,X
102
,X
180
,X
181
,X
182
,X
183
,
A
)-free
3d grid
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(4K
1
,P
4
)-free
(5,1)
(5-pan,T
2
,X
172
)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,1)-chordal ∩ bipartite
(6,2)
(6,2)-chordal ∩ bipartite
(A,C
5
,P
5
,
A
,house,parachute,parapluie)-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 ∩ bipartite
Apollonian network
B
0
-VPG ∩ bipartite
B
1
-CPG ∩ triangle-free
BW
3
-free ∩ modular
(C
4
∪ P
2
,C
5
,C
6
,K
2
∪ K
3
,K
2,3
,P
6
,W
4
,X
18
,X
5
,X
84
,
C
4
∪ P
2
,
C
6
,
P
6
,
W
4
,
X
18
,
X
5
,
X
84
,antenna,co-antenna,co-domino,co-fish,domino,fish)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,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
(C
4
,C
6
,C
8
,K
1,4
,odd-cycle)-free ∩ planar
(C
4
,C
6
,odd-cycle)-free
(C
4
,P
4
,dart)-free
(C
4
,P
4
,diamond,paw)-free
(C
4
,P
4
)-free
(C
4
,
P
3
,triangle)-free
(C
4
,
P
3
)-free
(C
4
,triangle)-free ∩ planar
C
4
-free ∩ C
6
-free ∩ bipartite
(C
5
,C
6
∪ K
1
,C
7
,K
3,3
∪ K
1
,K
3,3
-e ∪ K
1
,
K
5
- e
,domino ∪ K
1
,triangle)-free
(C
5
,C
6
,P
6
,X
17
,X
18
,X
5
,X
98
,
C
6
,
P
6
,antenna,domino)-free
(C
5
,C
6
,P
6
,triangle)-free
(C
5
,K
2
∪ K
3
,K
2,3
,P,P
2
∪ P
3
,P
5
,
P
,
P
2
∪ P
3
,co-fork,fork,house)-free
(C
5
,P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(C
5
,P,P
5
,
P
,co-fork,fork,house)-free
(C
5
,P,P
5
,
P
,house)-free
(C
5
,P,P
5
,house)-free
(C
5
,P
5
,
P
,house)-free
(C
5
,P
5
,co-fish,fish,house)-free
(C
5
,P
5
,house)-free
(C
5
,S
3
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
3K
2
,
P
2
∪ P
4
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,S
3
,
3K
2
,
P
2
∪ P
4
)-free ∩ P
4
-tidy
(C
5
,XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
(C
5
,co-butterfly,co-diamond,triangle)-free
C
5
-free ∩ P
4
-extendible
C
5
-free ∩ P
4
-tidy
C
5
-free ∩ matrogenic
C
6
-free ∩ modular
(C
n+4
∪ 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
,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
,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
,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
,bull,dart,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
(C
n+6
,odd-cycle)-free
Delaunay
Dilworth 1
Dilworth 2
(E,odd-cycle)-free
E-free ∩ bipartite
E-free ∩ planar
Gabriel
HHD-free ∩ co-HHD-free
HHDbicycle-free
Halin
Hilbertian
H
n,q
grid
(K
1,4
,odd-cycle)-free
(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
2,3
-free ∩ hereditary modular
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
(K
5
,X
126
,X
174
,
3K
2
)-minor-free
Laman ∩ planar
Matula perfect
Meyniel ∩ co-Meyniel
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
-laden
P
4
-lite
P
4
-reducible
P
4
-sparse
P
4
-tidy ∩ (S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
P
4
-tidy ∩ balanced
P
4
-tidy ∩ hereditary clique-Helly ∩ perfect
P
4
-tidy ∩ perfect
(P
5
,S
3
,
A
,
E
,
X
1
,anti-hole,co-domino,co-rising sun,net)-free
(P
5
,bull)-free ∩ interval
(P
6
,X
10
,X
11
,X
12
,X
13
,X
14
,X
15
,X
5
,X
6
,X
7
,X
8
,X
9
,
C
6
,
P
6
,antenna,hole)-free
P
6
-free ∩ chordal bipartite
(P
7
,odd-cycle,star
1,2,3
,sunlet
4
)-free
(P
7
,odd-cycle,star
1,2,3
)-free
(P
7
,odd-cycle)-free
P
7
-free ∩ bipartite
PURE-2-DIR
(S
3
,
C
n+4
,co-claw,net)-free
(S
3
,claw,net)-free ∩ chordal
(S
3
,net)-free ∩ split
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(T
2
,X
2
,X
3
,hole,triangle)-free
(T
2
,X
205
,X
206
,X
207
,X
208
,even-hole,odd-cycle)-free
(T
2
,cycle)-free
(T
3
,X
81
,cycle)-free
(T
3
,cycle)-free
Urquhart
V-perfect
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X
177
,odd-cycle)-free
(X
79
,X
80
)-free ∩ modular
(XC
1
,XC
2
,XC
3
,XC
4
,XC
5
,XC
6
,XC
7
,XC
8
)-free
(XC
11
,odd-cycle)-free
(XC
11
,odd-cycle)-free ∩ planar
(XC
12
,cycle)-free
(XC
12
,triangle)-free ∩ planar
(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
(
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
,odd-hole,paw)-free
(
C
n+4
,
T
2
,
X
31
,co-XF
2
n+1
,co-XF
3
n
)-free
(
C
n+4
,bull,house)-free
(
C
n+4
,co-claw,co-gem,house)-free
(
P
3
,triangle)-free
P
3
-free
(
T
2
,co-cycle)-free
absolute bipartite retract
almost CIS
almost median
almost tree (1)
almost-split
astral triple-free
b-perfect ∩ chordal
balanced ∩ paw-free
bar visibility
bi-cograph
biconvex
binary Hamming
binary tree
binary tree ∩ partial grid
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ distance-hereditary
bipartite ∩ girth>=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ grid intersection
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ module-composed
bipartite ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ unit grid intersection
bipartite ∩ weakly chordal
bipartite chain
bipartite permutation
bipartite tolerance
bisplit
bisplit ∩ triangle-free
book thickness 2
(bull,house,odd-hole)-free
cactus
caterpillar
chordal ∩ co-chordal
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ cograph
chordal ∩ comparability
chordal ∩ hamiltonian ∩ planar
chordal ∩ maximal planar
chordal ∩ planar
chordal ∩ proper circular arc
chordal ∩ unit circular arc
chordal bipartite
circle graph with equator
circular arc ∩ cograph
circular arc ∩ comparability
circular convex bipartite
circular interval
circular permutation
(claw ∪ 3K
1
,odd-cycle)-free
(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-bipartite ∩ proper circular arc
co-bithreshold ∩ split
co-bounded tolerance
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-cluster
co-comparability ∩ comparability
co-interval
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
co-probe threshold
co-proper interval bigraph
co-trapezoid
co-trivially perfect
co-trivially perfect ∩ trivially perfect
cograph
cograph ∩ interval
cograph ∩ split
coin
comparability
comparability ∩ distance-hereditary
comparability ∩ split
comparability ∩ weakly chordal
comparability graphs of arborescence orders
comparability graphs of dimension 2 posets
comparability graphs of dimension 3 posets
comparability graphs of dimension 4 posets
comparability graphs of dimension d posets
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension 2, height 2
comparability graphs of posets of interval dimension 2, height 3
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete
complete bipartite
complete multipartite
complete split
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cubical
cycle-free
difference
disjoint union of stars
disk contact
domination perfect ∩ planar
(domino,gem,hole,house,net)-free
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
(fork,odd-cycle)-free
genus 0
grid
grid graph
grid graph ∩ maximum degree 3
half
half-disk Helly
hamiltonian ∩ planar
hamiltonian ∩ split
hereditary Matula perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary median
hereditary modular
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
hole-free ∩ planar
homogeneously representable
homothetic triangle contact
hypercube
independent module-composed
indifference
indifference ∩ split
intersection graph of nested intervals
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-outerplanar
k-path graph, fixed k
k-tree, fixed k
leaf power ∩ min leaf power
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
matroidal
maxibrittle
maximal outerplanar
maximal planar
maximum degree 1
maximum degree 3 ∩ planar ∩ triangle-free
median
median ∩ planar
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
(odd-cycle,star
1,2,3
,sunlet
4
)-free
(odd-cycle,star
1,2,3
)-free
odd-cycle-free
(odd-hole,paw)-free
odd-hole-free ∩ planar
outerplanar
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 3d grid
partial 4-tree
partial bar visibility
partial cube
partial grid
partial k-tree, fixed k
paw-free ∩ perfect
perfect ∩ planar
perfect ∩ triangle-free
perfect elimination bipartite
perfectly colorable
permutation
permutation ∩ split
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
premedian
probe bipartite chain
probe co-trivially perfect ∩ probe trivially perfect
probe complete
probe interval ∩ tree
probe interval bigraph
probe threshold
probe threshold ∩ split
proper Helly circular arc
proper circular arc
proper interval
proper interval bigraph
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
quasi-threshold
relative neighbourhood graph
semi-median
semicircular
series-parallel
solid grid graph
solid triangular grid graph
split
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
star convex
starlike
starlike threshold
strict 2-threshold
strict B
1
-VCPG
subhamiltonian
superbrittle
superfragile
threshold
threshold signed
tolerance ∩ tree
tolerance ∩ triangle-free
tree
tree convex
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
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
(0,2)-graph
(0,3)-colorable
(1,2)-colorable
(1,2)-polar
1-DIR
1-bounded tripartite
(2,0)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
2-DIR
2-connected ∩ (4-fan,C
n+4
,K
5
- e,S
3
,
H
,
K
3
∪ 2K
1
)-free
2-split
2-split ∩ perfect
2-subdivision
2-thin
2-threshold
2-track
(2K
2
,4K
1
,co-claw,co-diamond)-free
(2K
2
,C
4
)-free
(2K
2
,C
5
,
C
6
,
C
7
,
C
8
,
XC
11
,co-claw,co-diamond)-free
(2K
2
,C
5
,
T
2
)-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
,co-claw,co-diamond)-free
(2K
2
,house)-free
(2K
2
,odd anti-hole)-free
2K
2
-free ∩ probe cograph
(2K
3
+ e,5-pan,A,C
6
,E,K
3,3
-e,P
6
,R,X
166
,X
167
,X
169
,X
170
,X
171
,X
172
,X
18
,X
37
,X
45
,X
5
,X
58
,X
84
,X
95
,X
98
,
5-pan
,
A
,
C
6
,
E
,
P
6
,
R
,
X
166
,
X
167
,
X
169
,
X
170
,
X
171
,
X
172
,
X
18
,
X
37
,
X
45
,
X
5
,
X
58
,
X
84
,
X
95
,
X
98
,antenna,co-antenna,co-domino,co-fish,co-twin-C
5
,co-twin-house,domino,fish,twin-C
5
,twin-house)-free
(2K
3
+ e,C
5
,C
6
,P
6
,X
5
,
2P
4
,
A
,
C
6
,
C
7
,
E
,
P
7
,
R
,
X
1
,
X
103
,
X
5
,
X
58
,
X
84
,
X
98
,antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet
4
)-free
(2K
3
+ 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
,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
,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
6
)-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-mino
(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
,butterfly,diamond)-free
(3K
1
,
K
2
∪ claw
)-free
(3K
1
,
P
6
)-free
(3K
1
,
X
172
)-free
(3K
1
,co-fork)-free
(3K
1
,house)-free
(3K
2
,A,C
4
∪ 2K
1
,E,P
2
∪ P
3
,R,
K
5
- e
,co-claw,net,odd anti-hole,twin-house)-free
(3K
2
,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
,E,P
2
∪ P
4
,net,odd anti-hole,odd-hole)-free
(3K
2
,
P
,co-gem,house)-free
(3K
2
,co-paw,odd anti-hole)-free
(3K
2
,triangle)-free
(3K
3
,C
n+4
)-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-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-fan,K
1,4
,W
4
,W
5
,
A ∪ K
1
,
co-fork ∪ K
1
,
gem ∪ K
1
,
net ∪ K
1
)-free
4-leaf power
4-regular
4-regular ∩ hamiltonian
(4K
1
,C
7
,S
3
,X
175
,X
176
,X
42
,
X
36
,claw,co-antenna,net,odd anti-hole)-free
(4K
1
,C
7
,X
195
,X
196
,X
38
,X
39
,
W
5
,
X
194
,
X
86
,
X
88
,
X
89
,
X
90
,house)-free
(4K
1
,C
7
,X
38
,X
39
,
K
3,3
∪ K
1
,
W
4
∪ K
1
,
W
5
,
X
86
,
X
87
,
X
88
,
X
89
,
X
90
,butterfly ∪ K
1
,diamond)-free
(4K
1
,K
4
)-free
(4K
1
,
C
n+4
)-free
(4K
1
,co-claw,co-diamond)-free
(4K
1
,gem)-free
(4K
1
,house)-free
(4K
1
,odd anti-hole,odd-hole)-free
(5,2)-chordal
(5,2)-crossing-chordal
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
5-colorable
5-leaf power
5-leaf power ∩ distance-hereditary
(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-regular
5-regular ∩ hamiltonian
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
(7,3)
(7,4)
(8,4)
(9,6)
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,
W
5
,co-claw,twin-C
5
,twin-house)-free
(A,C
4
∪ 2K
1
,P
2
∪ P
3
,R,
K
5
- e
,co-claw,odd anti-hole,twin-house)-free
(A,C
5
,C
6
,K
2
∪ K
3
,K
3,3
,K
3,3
+e,K
3,3
-e,P
6
,X
5
,X
98
,
2P
3
,
C
6
,
C
7
,
W
4
,
X
84
,
X
95
,co-butterfly,co-fish,domino,fish)-free
(A,C
5
,C
6
,P
6
,domino,house)-free
(A,E,S
3
,X
1
,domino,hole,house,net,rising sun)-free
(A,H,K
3,3
,K
3,3
-e,T
2
,X
18
,X
45
,domino,triangle)-free
(A,H,K
3,3
,X
45
,triangle)-free
(A,P
6
,clique wheel,domino,hole,house)-free
AC
AT-free ∩ chordal
B
0
-CPG
B
0
-VPG
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
Berge
Berge ∩ bull-free
Berge ∩ claw-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,K
1,4
,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,X
85
,triangle)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,H,X
85
,triangle)-free ∩ K
1,4
-free
(C
4
,C
5
,C
6
,C
7
,C
8
,K
1,4
,K
5
,K
5
- e,
K
3
∪ 2K
1
,
P
3
∪ 2K
1
,
claw ∪ K
1
,butterfly,cricket,dart,gem)-free
(C
4
,C
5
,C
6
,C
7
,C
8
,XC
11
,claw,diamond)-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
,K
4
,claw,diamond)-free
(C
4
,P
5
)-free
(C
4
,P
6
)-free
(C
4
,S
3
)-free
(C
4
,X
91
,claw)-free
(C
4
,
A
,
H
)-free
(C
4
,claw,diamond)-free
(C
4
,co-claw)-free
(C
4
,diamond)-free
(C
4
,odd-hole)-free
(C
4
,triangle)-free
C
4
-free
C
4
-free ∩ co-comparability
C
4
-free ∩ induced-hereditary pseudo-modular
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
,
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
,K
3,3
-e,T
2
,X
18
,X
94
,domino,triangle)-free
(C
5
,P,
P
,bull,co-fork,gem,house)-free
(C
5
,P,co-fork,fork,gem,house)-free
(C
5
,P
2
∪ P
3
,house)-free
(C
5
,P
5
,
A
,
C
6
,
P
6
,co-domino)-free
(C
5
,P
5
,
C
6
,
C
7
,
C
8
,
P
8
,
X
19
,
X
20
,
X
21
,
X
22
,co-gem)-free
(C
5
,P
5
,
P
,co-fork,co-gem,fork)-free
(C
5
,P
5
,
P
2
∪ P
3
)-free
(C
5
,P
5
,gem)-free
(C
5
,P
6
,
P
6
)-free
(C
5
,S
3
,X
11
,
3K
2
,
C
7
,
P
2
∪ P
4
,
X
173
)-free ∩ co-line
(C
5
,bull,co-gem,gem)-free
(C
5
,co-gem,gem)-free
(C
5
,co-gem,house)-free
(C
5
,house)-free
(C
6
,K
2
∪ K
3
,X
103
,X
37
,X
88
,X
90
,
C
n+4
∪ K
1
,
T
2
,
net ∪ K
1
,co-diamond,co-domino,co-eiffeltower,co-twin-C
5
)-free
(C
6
,K
2
∪ K
3
,X
37
,X
90
,
C
n+4
∪ K
1
,
T
2
,
W
n+4
,
X
31
,co-XF
2
n+1
,co-XF
3
n
,co-domino,co-twin-C
5
)-free
(C
6
,P
6
,
P
6
,
X
10
,
X
11
,
X
12
,
X
13
,
X
14
,
X
15
,
X
5
,
X
6
,
X
7
,
X
8
,
X
9
,anti-hole,co-antenna)-free
(C
6
,S
3
,
C
n+4
∪ K
1
,
W
4
,
W
5
,co-claw,net)-free
(C
6
,
C
6
)-free murky
(C
6
,house)-free
(C
6
,triangle)-free
CPG
(C
n+3
∪ K
1
,diamond,paw)-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
205
,
X
206
,
X
207
,
X
208
,
odd-cycle ∪ K
1
,even anti-hole,net)-free
(C
n+4
,H)-free
(C
n+4
,S
3
∪ K
1
,
X
103
,claw,eiffeltower,net ∪ K
1
)-free
(C
n+4
,S
3
,net)-free
(C
n+4
,S
3
)-free
(C
n+4
,T
2
,X
31
,XF
2
n+1
,XF
3
n
)-free
(C
n+4
,T
2
,XF
2
n+1
)-free
(C
n+4
,T
2
,net)-free
(C
n+4
,X
102
,X
204
,
P
3
∪ 2K
1
,gem)-free
(C
n+4
,X
59
,longhorn)-free
(C
n+4
,
K
3
∪ 3K
1
,dart,gem)-free
(C
n+4
,claw,gem)-free
(C
n+4
,claw,net)-free
(C
n+4
,claw)-free
(C
n+4
,dart,gem)-free
(C
n+4
,diamond)-free
(C
n+4
,gem)-free
(C
n+4
,odd-sun)-free
(C
n+4
,sun)-free
C
n+4
-free
(C
n+6
,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
D
Dilworth 3
Dilworth 4
(E,triangle)-free
EPT ∩ chordal
F
n
grid
Gallai
Gallai-perfect
(H,K
3
∪ 2K
1
,
C
n+4
,
K
5
- e
,
X
100
,
X
101
,
X
102
,co-4-fan,net)-free
(H,K
3
∪ 2K
1
,
C
n+4
,
K
5
- e
,co-4-fan,net)-free
(H,triangle)-free
HH-free
HHD-free
HHDA-free
HHDG-free
HHDS-free
HHG-free
HHP-free
Helly 2-acyclic subtree
Helly ∩ bridged
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly chordal
Helly chordal ∩ clique-chordal
Helly circle
Helly circular arc
Helly circular arc ∩ (
C
7
,odd-hole)-free
Helly circular arc ∩ concave-round
Helly circular arc ∩ perfect
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
(K
1,4
,diamond)-free
(K
1,4
,paw)-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
,X
90
,
C
n+4
∪ K
1
,
T
2
,co-domino,co-paw,co-twin-C
5
)-free
(K
2
∪ K
3
,
P
,
X
163
,
X
95
,co-diamond,house)-free
(K
2
∪ K
3
,
P
,anti-hole)-free
(K
2
∪ K
3
,
P
,house)-free
(K
2
∪ K
3
,house)-free
(K
2
∪ claw,triangle)-free
(K
2,3
,P,P
5
,X
163
,X
95
,diamond)-free
(K
2,3
,X
37
,X
38
,diamond,domino,house,twin-C
5
)-free
(K
2,3
,diamond)-free
(K
2,3
,diamond)-free ∩ weakly modular
(K
3
∪ 3K
1
,
C
n+4
,co-dart,co-gem)-free
(K
3
∪ P
3
,
C
6
,
P
,
P
7
,
X
37
,
X
41
)-free
(K
3,3
∪ K
1
,K
4
,W
4
∪ K
1
,W
5
,X
86
,X
87
,X
88
,X
89
,X
90
,
C
7
,
X
38
,
X
39
,
butterfly ∪ K
1
,co-diamond)-free
(K
3,3,3
,
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
,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
,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
,claw,diamond)-free
(K
4
,co-gem)-free
(K
4
,odd anti-hole,odd-hole)-free
(K
4
,odd anti-hole,odd-hole)-free ∩ dually chordal
K
4
-free
K
4
-free ∩ dually chordal ∩ perfect
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
Laman
Meyniel
Meyniel ∩ weakly chordal
Mycielski
N
*
-perfect
(P,P
5
,S
3
,
P
,co-fork,fork,house,net)-free
(P,P
5
,
3K
2
,gem)-free
(P,P
5
,
P
,co-fork,fork,house)-free
(P,P
5
,co-fork)-free
(P,
P
,co-fork,fork)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-fork)-free
(P,co-gem,house)-free
(P
2
∪ P
3
,house)-free
(P
2
∪ P
4
,triangle)-free
(P
3
∪ 2K
1
,
C
n+4
,
X
102
,
X
204
,co-gem)-free
P
4
-brittle
P
4
-comparability
P
4
-extendible
P
4
-indifference
P
4
-simplicial
P
4
-tidy
(P
5
,S
3
,anti-hole,co-domino,co-gem)-free
(P
5
,
A
,
P
6
,anti clique wheel,anti-hole,co-domino)-free
(P
5
,
A
,anti-hole,co-domino)-free
(P
5
,
C
6
)-free ∩ weakly chordal
(P
5
,
P
,anti-hole)-free
(P
5
,
P
,gem)-free
(P
5
,
P
2
∪ P
3
)-free
(P
5
,anti-hole,co-bicycle,co-domino)-free
(P
5
,anti-hole,co-domino,co-gem)-free
(P
5
,anti-hole,co-domino,co-sun)-free
(P
5
,anti-hole,co-domino)-free
(P
5
,anti-hole,co-gem)-free
(P
5
,anti-hole)-free
(P
5
,bull,co-fork)-free
(P
5
,bull,house)-free
(P
5
,bull,odd anti-hole)-free
(P
5
,co-fork,house)-free
(P
5
,co-fork)-free
(P
5
,diamond)-free
(P
5
,fork,house)-free
(P
5
,gem)-free
(P
5
,house)-free
(P
5
,triangle)-free
P
5
-free ∩ tripartite
P
5
-free ∩ weakly chordal
(P
6
,triangle)-free
P
6
-free ∩ tripartite
PI
PI
*
PURE-3-DIR
(S
3
,T
2
,X
2
,X
3
,
C
n+4
∪ K
1
,
C(n,k)
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,T
2
,X
2
,X
3
,
C
n+4
∪ K
1
,
S
3
∪ K
1
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,T
2
,X
205
,X
206
,X
207
,X
208
,
C
n+4
∪ K
1
,
S
3
∪ K
1
,
X
42
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,
3K
2
,
E
,
P
2
∪ P
4
,odd anti-hole,odd-hole)-free
(S
3
,
3K
2
,
E
,
P
2
∪ P
4
)-free
(S
3
,
3K
2
,
E
,odd-hole)-free ∩ line
(S
3
,
C
n+4
∪ K
1
,
C(n,k)
,
W
4
,even-hole,odd-cycle ∪ K
1
)-free
(S
3
,
C
n+4
,
S
3
∪ K
1
,co-claw)-free
(S
3
,
C
n+4
,
T
2
)-free
(S
3
,
C
n+4
,co-claw)-free
(S
3
,
C
n+4
,net)-free
(S
3
,
C
n+6
,
X
37
,antenna,co-claw,co-sun)-free
(S
3
,co-claw,net)-free
(S
3
,co-claw)-free
(S
3
,net)-free ∩ chordal
(S
3
,net)-free ∩ extended P
4
-sparse
S
3
-free ∩ chordal
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
W
n+4
-free
(X
103
,
C
n+4
,
S
3
∪ K
1
,
net ∪ K
1
,co-claw,co-eiffeltower)-free
(X
12
,X
5
,X
95
,X
96
,X
97
,
X
12
,
X
5
,
X
95
,
X
96
,
X
97
,
claw ∪ triangle
,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X
172
,triangle)-free
(X
34
,X
36
,XF
2
n+1
,XF
3
n
,
C
n+4
,co-XF
1
2n+3
,co-XF
6
2n+2
)-free
(X
37
,diamond,even-cycle)-free
(X
38
,gem,house)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free ∩ normal circular arc ∩ quasi-line
XC
10
-free
XC
10
-free ∩ pseudo-modular
XC
10
-free ∩ weakly modular
(XC
11
,claw,diamond)-free
(XC
12
,triangle)-free
XC
13
-free
(XC
7
,
XC
1
,
XC
2
,
XC
3
,
XC
4
,
XC
5
,
XC
6
,
XC
8
)-free
XC
9
-free
(XZ
11
,XZ
12
,XZ
13
,XZ
14
,XZ
6
,XZ
7
,XZ
8
,XZ
9
,
XZ
11
,
XZ
12
,
XZ
13
,
XZ
14
,
XZ
6
,
XZ
7
,
XZ
8
,
XZ
9
)-free
β-perfect
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
cal C(G)-perfect
(
3K
2
,
C
6
,
P
7
,
X
164
,
X
165
,
sunlet
4
,odd anti-cycle)-free
(
A
,
P
6
,co-domino)-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
,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
,
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
(
E
,
P
)-free
(
E
,odd anti-cycle)-free
(
K
1,4
,
P
,co-fork,house)-free
(
K
1,4
,house)-free
(
K
1,4
,odd anti-cycle)-free
K
2
∪ claw
-free
(
P
,
P
7
)-free
(
P
,
P
8
)-free
(
P
,
T
2
)-free
(
P
,
star
1,2,3
)-free
(
P
,butterfly,fork,gem)-free
(
P
,co-star
1,2,4
)-free
(
P
,co-star
1,2,5
)-free
(
P
,fork,gem)-free
(
P
,fork,house)-free
(
P
,house)-free
(
P
6
,
X
30
,
X
8
)-free
(
P
6
,co-claw)-free
P
6
-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
3
,
X
81
,co-cycle)-free
(
T
3
,co-cycle)-free
(
W
4
,co-claw,co-gem,odd anti-hole)-free
(
W
4
,co-claw,co-gem)-free
(
W
4
,co-claw)-free
(
X
177
,odd anti-cycle)-free
(
X
82
,
X
83
,house)-free
(
X
91
,co-claw)-free
(
XC
11
,co-claw,co-diamond)-free
(
XC
11
,odd anti-cycle)-free
(
XC
12
,co-cycle)-free
(
claw ∪ 3K
1
,odd anti-cycle)-free
(n+4)-pan
-free
odd-cycle ∪ K
1
-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
absorbantly perfect
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
alternation
(anti-hole,bull,odd-hole)-free
(anti-hole,co-domino,odd anti-cycle)-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
apex
b-perfect
balanced
balanced ∩ chordal
balanced ∩ co-line
balanced ∩ line
basic 4-leaf power
basic perfect
biclique separable
biclique-Helly
bip
*
bipartable
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ double split ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ split
biplanar
bipolarizable
bithreshold
bitolerance
block
block duplicate
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 1
boxicity 2
boxicity 2 ∩ co-bipartite
bridged
bridged ∩ clique-Helly
brittle
building-free
building-free ∩ even-signable
building-free ∩ odd-signable
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,hole,odd anti-hole)-free
(bull,house)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
(butterfly,gem)-free
caterpillar arboricity <= 2
charming
chordal
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-comparability
chordal ∩ diametral path
chordal ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ domination perfect
chordal ∩ domino
chordal ∩ dually chordal
chordal ∩ gem-free
chordal ∩ hamiltonian
chordal ∩ hereditary clique-Helly
chordal ∩ hereditary dominating pair
chordal ∩ irredundance perfect
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ probe diamond-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal-perfect
circle
circle ∩ diamond-free
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular arc
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular perfect
circular strip
(claw,co-claw)-free
(claw,diamond,odd-hole)-free
(claw,diamond)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ mock threshold
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
clique separable
clique-perfect ∩ triangle-free
cliquewidth 3
cliquewidth 4
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P
4
-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-biclique separable
co-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bithreshold
(co-butterfly,co-claw)-free
co-chordal
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,co-paw)-free
(co-claw,house)-free
(co-claw,odd anti-cycle)-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 ∩ tolerance
co-comparability ∪ comparability
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 2
co-comparability graphs of posets of interval dimension d
(co-cricket,house)-free
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-forest-perfect
(co-fork,hole)-free
(co-fork,house)-free
(co-fork,odd anti-cycle)-free
co-fork-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-interval filament
co-interval mixed
co-leaf power
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
(co-paw,paw)-free
(co-paw,triangle)-free
co-perfectly orderable
co-probe cograph
co-quasi-line
co-strongly chordal
co-threshold tolerance
co-tolerance
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
complete Hamming
concave-round
convex-round
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cycle-bicolorable
d-trapezoid
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
directed path
distance-hereditary
domination
domination perfect ∩ triangle-free
domino
(domino,gem,house)-free
(domino,gem,house)-free ∩ pseudo-modular
double split
doubled
doubly chordal
dually chordal ∩ tripartite
even-cycle-free
even-hole-free ∩ probe chordal
extended P
4
-laden
extended P
4
-reducible
extended P
4
-sparse
forest-perfect
(fork,house)-free
(fork,triangle)-free
fuzzy circular interval
fuzzy linear interval
gem-free
generalized split
generalized strongly chordal
generically minimally rigid
genus 1
geodetic
girth>=9
good
grid intersection
gridline
hamiltonian ∩ interval
hereditary Helly
hereditary N
*
-perfect
hereditary biclique-Helly
hereditary clique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ self-clique
hereditary disk-Helly
hereditary dismantlable
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary sat
(hole,odd anti-hole)-free
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
intersection graphs of parallelograms (squares)
interval
interval filament
k-polygon
kernel solvable
leaf power
leaf power ∪ min leaf power
line
line ∩ mock threshold
line ∩ perfect
line ∩ well covered
line graphs of Helly hypergraphs of rank 3
line graphs of acyclic multigraphs
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 arboricity <= 2
linear domino
linear domino ∩ maximum degree 4
locally bipartite
locally chordal
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally perfect
locally split
matrogenic
max-tolerance
maximal clique irreducible
maximum degree 3
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
min leaf power
minimally imperfect
mock threshold
module-composed
monopolar
multitolerance
murky
nearly bipartite
neighbourhood chordal
neighbourhood perfect
neighbourhood-Helly ∩ triangle-free
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-cycle ∪ K
1
-free
odd-hole-free ∩ pretty
odd-signable ∩ triangle-free
open-neighbourhood-Helly
opposition
overlap
parallelepiped
parity
partial rectangle visibility
partner-limited
paw-free
perfect
perfect ∩ split-neighbourhood
perfectly 1-transversable
perfectly contractile
perfectly orderable
power-chordal
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P
4
-reducible
probe P
4
-sparse
probe bipartite distance-hereditary
probe block
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe cograph
probe diamond-free
probe distance-hereditary
probe interval
probe proper interval
probe ptolemaic
probe split
probe strongly chordal
probe trivially perfect
probe unit interval
proper chordal
proper tolerance
pseudo-median
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-Meyniel
quasi-brittle
quasi-line
quasi-median
quasi-parity
quasitriangulated
rectagraph
rectangle intersection
rectangle visibility
restricted block duplicate
rigid circuit
rooted directed path
semi-P
4
-sparse
semi-square intersection
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
spider graph
split-neighbourhood
split-perfect
square of tree
strict quasi-parity
strictly chordal
strictly clique irreducible
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly even-signable
strongly odd-signable
strongly orderable
strongly perfect
substar
sun-free ∩ weakly chordal
superperfect
thick tree
thickness <= 2
threshold tolerance
tolerance
toroidal
totally unimodular
trapezoepiped
trapezoid
tree-cograph
tree-perfect
triangle-free
triangulated
tripartite
undirected path
unimodular
unipolar
unit 2-track
unit Helly circle
unit disk
unit grid intersection
unit tolerance
very strongly perfect
weak bipolarizable
weak bisplit
weak rectangle visibility
weakly chordal
weakly geodetic
weakly median
well-partitioned chordal
wing-triangulated
back to top
GI-complete
back to top
NP-hard
back to top
NP-complete
2-SEG
2-circular arc
2-circular track
2-connected
2-edge-connected
2-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
,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
5
,
C
6
,
C
7
,
C
8
)-free
(2K
2
,C
5
,
C
6
,net)-free
(2K
2
,C
5
)-free
(2K
2
,claw)-free
(2K
2
,co-diamond)-free
(2K
2
,net)-free
2K
2
-free
(2K
3
,2K
3
+ e,
A
,
H
,
X
45
,
XZ
5
,co-domino)-free
(2K
3
,3K
1
,
A
,
H
,
X
45
)-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
2P
3
-free
3-Helly
3-circular track
3-interval
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
,
K
1,5
)-free
(3K
1
,
XC
12
)-free
(3K
1
,co-cross)-free
3K
1
-free
(3K
2
,C
5
,C
7
,P
2
∪ P
4
,X
173
,
X
11
,net)-free
(3K
2
,C
5
,P
2
∪ P
4
,net)-free
(3K
2
,E,P
2
∪ P
4
,net)-free
(4,0)-colorable
(4K
1
,net)-free
4K
1
-free
(5,2)
(5-pan,T
2
,X
172
)-free
5K
1
-free
(6,1)-chordal
(6,1)-even-chordal
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,H,K
3,3
,K
3,3
-e,X
45
,XZ
5
,domino)-free
(A,H,K
3,3
,X
45
,X
46
,X
47
,X
48
,X
49
,X
50
,X
51
,X
52
,X
53
,X
54
,X
55
,X
56
,X
57
,
X
42
)-free
(A,P
6
,domino)-free
AT-free
AT-free ∩ claw-free
B
1
-VPG
B
2
-VPG
B
3
-VPG
BW
3
-free
B
k
-VPG
(C
5
,P,P
5
,
P
,bull,co-gem,fork)-free
(C
5
,P
5
)-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
,
C
6
)-free
C
6
-free
CONV
(C
n+6
,T
2
,X
2
,X
3
,X
30
,X
31
,X
32
,X
33
,X
34
,X
35
,X
36
,X
37
,X
38
,X
39
,X
40
,X
41
,XF
2
n+1
,XF
3
n
,XF
4
n
)-free
(C
n+6
,X
37
,claw,co-antenna,net,sun)-free
C
n+6
-free
C
n+7
-free
(E,P)-free
E-free
Hamiltonian hereditary
Helly
(K
1,4
,P,P
5
,fork)-free
(K
1,4
,P
5
)-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
,co-diamond)-free
K
2
∪ K
3
-free
K
2
∪ claw-free
(K
2,3
,P,P
5
)-free
(K
2,3
,P,hole)-free
(K
2,3
,P
5
)-free
K
2,3
-free
(K
3
∪ 2K
1
,
K
3
∪ 2K
1
,bull,co-cricket,co-dart,cricket,dart)-free
(K
3,3
,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
N
*
(P,P
5
)-free
(P,P
7
)-free
(P,P
8
)-free
(P,T
2
)-free
(P,star
1,2,3
)-free
(P,star
1,2,4
)-free
(P,star
1,2,5
)-free
P-free
(P
2
∪ P
3
,P
3
∪ 2K
1
,X
188
,X
214
,
W
4
,
X
102
,
X
204
,
X
209
,
X
210
,
X
212
,
X
213
,
X
215
,
X
216
,
X
217
,
X
218
,
X
86
,co-gem)-free
P
2
∪ P
4
-free
P
4
-bipartite
(P
5
,X
82
,X
83
)-free
(P
5
,
C
6
)-free
(P
5
,
X
38
,co-gem)-free
(P
5
,bull)-free
(P
5
,claw)-free
(P
5
,co-domino,co-gem)-free
(P
5
,cricket)-free
(P
5
,fork)-free
P
5
-free
(P
6
,X
30
,X
8
)-free
(P
6
,claw)-free
P
6
-free
P
7
-free
(S
3
,S
4
,net)-free
(S
3
,T
2
,X
205
,X
206
,X
207
,X
208
,
X
42
)-free
(S
3
,claw,net)-free
(S
3
,net)-free
(S
3
,net)-free ∩ sun-free
S
3
-free
SEG
VPG
(X
30
,XZ
1
,XZ
4
,longhorn)-free
(X
79
,X
80
)-free
(X
91
,claw)-free
BW
3
-free
C
6
-free
(
C
7
,odd-hole)-free
(
K
1,4
,co-diamond)-free
(
K
1,4
,co-paw)-free
K
1,4
-free
(
P
,fork)-free
P
-free
W
2n+3
-free
(
W
4
,
W
5
,co-butterfly)-free
(
W
4
,co-gem)-free
W
n+4
-free
(
X
30
,
XZ
1
,
XZ
4
,co-longhorn)-free
(
X
79
,
X
80
)-free
XC
10
-free
XC
11
-free
XC
12
-free
XC
13
-free
all-4-simplicial
almost claw-free
balanced 2-interval
(bull,fork)-free
bull-free
(butterfly,claw)-free
(claw,net)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ upper domination perfect
clique graphs
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
co-2-subdivision
co-building-free
(co-butterfly,co-gem)-free
co-diamond-free
co-domino-free
co-gem-free
co-hereditary clique-Helly
co-paw-free
co-planar
co-sun-free
cop-win
diametral path
disk-Helly
dismantlable
domination perfect
domino-free
dually chordal
even-hole-free
even-signable
fork-free
hamiltonian
hereditary dominating pair
hole-free
homogeneously orderable
irredundance perfect
irredundance perfect with ir(G)<= 4
k-SEG
locally connected
(n+4)-pan-free
nK
2
-free, fixed n
nP
3
-free, fixed n
neighbourhood-Helly
net-free
odd co-sun-free
odd-hole-free
odd-sun-free
(p,q<=2)-colorable
perfect cochromatic
perfect connected-dominant
polar
probe AT-free
pseudo-modular
string
strong domination perfect
sun-free
unit 2-circular arc
unit 2-interval
unit 3-circular track
unit 3-interval
unit 3-track
universally signable
upper domination perfect
upper irredundance perfect
weak dominating pair
back to top
coNP-complete
back to top
Open
unit 2-circular track
back to top
Unknown to ISGCI
(1,2)-split
1-string
(2,2)-interval
2-connected ∩ (P
6
,claw)-free
2-strongly regular
(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
,2K
3
+ e,3K
1
,
A
,
H
,
T
2
,
X
18
,
X
45
,co-domino)-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
2
,E,net,odd anti-hole)-free
(6,2)-chordal
(6,3)
(7,5)
(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
Birkhoff
Bouchet
(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
7
,odd anti-hole)-free
CIS
Deza
EPT
Hamilton-connected
Hamming
Helly ∩ reflexive
Helly subtree
K
1,4
-free ∩ almost claw-free ∩ locally connected
K
1,4
-free ∩ well covered
PURE-k-DIR
Raspail
(S
3
,
3K
2
,
E
,odd-hole)-free
(X
42
,
T
2
,
X
205
,
X
206
,
X
207
,
X
208
,net)-free
cal P
3
-perfect
2P
3
-free
(
5-pan
,
T
2
,
X
172
)-free
C
n+6
-free
C
n+7
-free
E
-free
P
2
∪ P
4
-free
P
7
-free
(
X
37
,co-diamond,even anti-cycle)-free
absolute reflexive retract
anti-hole-free
bigeodetic
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
circular trapezoid
claw-free ∩ locally connected
claw-free ∩ well covered
clique-Helly ∩ dismantlable ∩ reflexive
clique-perfect
co-β-perfect
co-circular perfect
(co-diamond,even anti-cycle)-free
disk
distance regular
distance regular of diameter 2
edge regular
equimatchable
even anti-cycle-free
even anti-hole-free
frame hereditary dominating pair
fully cycle extendable
graceful
harmonious
hereditary weakly modular
induced-hereditary pseudo-modular
interval enumerable
interval regular
interval regular of diameter 2
irredundance perfect with ir(G)=2
isometric-HH-free
isometric-hereditary pseudo-modular
k-DIR
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
line perfect
map
middle
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
normal
odd anti-hole-free
odd-signable
outer-string
(p,q)-colorable
(p,q)-split
p-connected
p-tree
pairwise compatibility
partitionable
path orderable
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe co-bipartite
probe co-comparability
probe comparability
probe permutation
(q,t)
reflexive
self-clique
self-complementary
strong asteroid free
strongly regular
subtree filament
subtree overlap
unbreakable
unigraph
visibility
walk regular
weakly modular
well covered
well-dominated
back to top
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