This problem
Linear
Polynomial
GI-complete
NP-hard
NP-complete
coNP-complete
Open
Unknown

Problem: Maximum cut

Definition:

(decision variant)

Input: A graph G in this class and an integer k.

Output: True iff the vertices of G can be partitioned into two sets A,B such that there are at least k edges in G with one endpoint in A and the other endpoint in B.

Linear

(0,2)-colorable
(0,2)-colorable ∩ chordal
(0,2)-graph ∩ bipartite
(0,3)-colorable ∩ chordal
1-bounded bipartite
2-bounded bipartite
2-outerplanar
2-terminal series-parallel
2-tree
2-tree ∩ probe interval
(2C₄,3K₂,C₆,E,P₂ ∪ P₄,P₆,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,odd-cycle)-free
2K₁-free
(2K₂,3K₁,C₄,P₄)-free
(2K₂,3K₁,P₃)-free
(2K₂,C₄,C₅,S₃,claw,net)-free
(2K₂,C₄,P₄,triangle)-free
(2K₂,C₅,triangle)-free
(2K₂,P₃,triangle)-free
(2K₂,P₃)-free
2K₂-free ∩ bipartite
3-tree
3-tree ∩ planar
(3K₁,C₄,P₃)-free
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,odd-cycle,sunlet₄)-free
3d grid
(6,1)-chordal ∩ bipartite
(6,2)-chordal ∩ bipartite
(A,T₂,odd-cycle)-free
AT-free ∩ bipartite
Apollonian network
B₀-VPG ∩ bipartite
BW₃-free ∩ modular
(C₄,C₆,C₈,K_1,4,odd-cycle)-free
(C₄,C₆,C₈,K_1,4,odd-cycle)-free ∩ planar
(C₄,C₆,odd-cycle)-free
(C₄,P₃,triangle)-free
C₄-free ∩ C₆-free ∩ bipartite
(C₅,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,K₅ - e,domino ∪ K₁,triangle)-free
(C₅,C₆,P₆,triangle)-free
(C₅,co-butterfly,co-diamond,triangle)-free
C₆-free ∩ modular
(C_n+4,K₄)-free
(C_n+6,odd-cycle)-free
(E,odd-cycle)-free
E-free ∩ bipartite
Halin
Hilbertian
(K_1,4,odd-cycle)-free
(K_1,4,odd-cycle)-free ∩ planar
(K_2,3,K₄)-minor-free
K_2,3-free ∩ hereditary modular
K₂-free
K₃-minor-free
K₄-minor-free
(K₅,X₁₂₆,X₁₇₄,3K₂)-minor-free
(P₃,triangle)-free
(P₄,cycle)-free
(P₄,triangle)-free
P₆-free ∩ chordal bipartite
(P₇,odd-cycle,star_1,2,3,sunlet₄)-free
(P₇,odd-cycle,star_1,2,3)-free
(P₇,odd-cycle)-free
P₇-free ∩ bipartite
PURE-2-DIR
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(T₂,X₂,X₃,hole,triangle)-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even-hole,odd-cycle)-free
(T₂,cycle)-free
(T₃,X₈₁,cycle)-free
(T₃,cycle)-free
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X₁₇₇,odd-cycle)-free
(X₇₉,X₈₀)-free ∩ modular
(XC₁₁,odd-cycle)-free
(XC₁₁,odd-cycle)-free ∩ planar
(XC₁₂,cycle)-free
(P₃,triangle)-free
absolute bipartite retract
almost median
almost tree (1)
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 ∩ triangle-free
cactus
caterpillar
chordal ∩ hamiltonian ∩ planar
chordal ∩ maximal planar
chordal ∩ planar
chordal bipartite
circular convex bipartite
(claw ∪ 3K₁,odd-cycle)-free
(claw,odd-cycle)-free
comparability graphs of posets of interval dimension 2, height 2
complete
complete bipartite
convex
cubical
cycle-free
difference
disjoint union of stars
(domino,hole,odd-cycle)-free
domino-free ∩ modular
(fork,odd-cycle)-free
grid
grid graph
grid graph ∩ maximum degree 3
half
half-disk Helly
hereditary X-chordal
hereditary absolute bipartite retract
hereditary median
hereditary modular
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
hypercube
independent module-composed
indifference ∩ split
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-outerplanar
k-path graph, fixed k
k-tree, fixed k
lobster
maximal outerplanar
maximum degree 1
median
median ∩ planar
modular
modular ∩ open-neighbourhood-Helly
(odd-cycle,star_1,2,3,sunlet₄)-free
(odd-cycle,star_1,2,3)-free
odd-cycle-free
outerplanar
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 3d grid
partial 4-tree
partial cube
partial grid
partial k-tree, fixed k
perfect ∩ triangle-free
perfect elimination bipartite
premedian
probe bipartite chain
probe interval ∩ tree
probe interval bigraph
proper interval bigraph
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
semi-median
series-parallel
solid grid graph
star convex
tolerance ∩ tree
tolerance ∩ triangle-free
tree
tree convex
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
unicyclic
unit interval bigraph

Polynomial

(2,0)-colorable ∩ chordal
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-leaf power
2-strongly regular ∩ planar
2-subdivision ∩ planar
(2K₂,C₄,C₅,H,S₃,X₁₆₀,X₁₅₉,net,rising sun)-free
(2K₂,C₄,C₅,S₃,X₁₅₉,X₁₆₀,H,co-rising sun,net)-free
(2K₂,C₄,C₅,S₃,co-claw,net)-free
(2K₂,C₄,C₅,claw,diamond)-free
(2K₂,C₄,C₅,co-claw,co-diamond)-free
(2K₂,C₄,P₄)-free
(2K₂,C₅,S₃,X₁₅₉,X₁₆₀,X₁₆₁,X₁₆₂,X₄₆,X₇₀,2P₃,3K₂,H,P₂ ∪ P₄,X₁,co-rising sun,house,net)-free
(2K₂,K_3,3,K_3,3+e,P₄,2P₃)-free
(2K₂,P₄,2P₃)-free
(2K₂,P₄,co-dart)-free
(2K₂,P₄,co-diamond,co-paw)-free
(2K₂,P₄)-free
2K₂-free ∩ probe cograph
2K₂-free ∩ probe trivially perfect
(2K₃ + e,A,C₅,C₆,E,H,K_3,3-e,P₆,R,S₃,X₁₆₆,X₁₆₇,X₁₆₈,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₆,X₉₈,A,C₆,E,H,P₆,R,X₁₆₆,X₁₆₇,X₁₆₈,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₆,X₉₈,antenna,co-antenna,co-cross,co-domino,co-fish,co-twin-house,cross,domino,fish,net,twin-house)-free
(2K₃,2P₃,C₄,K₃ ∪ P₃,P₄)-free
(2P₃,3K₂,C₄,C₅,H,P₂ ∪ P₄,P₅,S₃,X₁,X₁₆₀,X₁₅₉,X₁₆₁,X₁₆₂,X₄₆,X₇₀,net,rising sun)-free
(2P₃,C₄,P₄)-free
(2P₃,P₄)-free
3-leaf power
(3K₁,C₄,C₅)-free
(3K₁,C₅,K₅ - e,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,domino ∪ K₁)-free
(3K₁,C₅,C₆,P₆)-free
(3K₁,C₅,butterfly,diamond)-free
(3K₁,P₃)-free
(3K₁,P₄)-free
(3K₁,K₂ ∪ claw)-free
(3K₁,P₃)-free
(3K₁,P₆)-free
(3K₁,X₁₇₂)-free
(3K₁,co-fork)-free
(3K₁,house)-free
(3K₁,paw)-free
(3K₂,C₅,P₂ ∪ P₄,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,net)-free
(3K₂,P,co-gem,house)-free
4-leaf power
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(4K₁,K₄)-free
(4K₁,P₄)-free
(4K₁,C_n+4)-free
(5,1)
(5,2)-crossing-chordal
5-leaf power
5-leaf power ∩ distance-hereditary
(5-pan,T₂,X₁₇₂)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,2)
(7,3)
(7,4)
(8,4)
(9,6)
AC
B₁-CPG ∩ triangle-free
(C₄,C₅,C₆,C₇,C₈,K_1,4,K₅,K₅ - e,K₃ ∪ 2K₁,P₃ ∪ 2K₁,claw ∪ K₁,butterfly,cricket,dart,gem)-free ∩ planar
(C₄,C₅,C₆,C₇,C₈,XC₁₁,claw,diamond)-free
(C₄,C₅,C₆,C₇,C₈)-free ∩ maximum degree 3 ∩ planar
(C₄,C₅,K₄,diamond)-free ∩ planar
(C₄,K₄,claw,diamond)-free
(C₄,P₄,dart)-free
(C₄,P₄,diamond,paw)-free
(C₄,P₄)-free
(C₄,P₃)-free
(C₄,claw,diamond)-free
(C₄,triangle)-free ∩ planar
(C₅,K₂ ∪ K₃,K_2,3,P,P₂ ∪ P₃,P₅,P,P₂ ∪ P₃,co-fork,fork,house)-free
(C₅,P,P₅,S₃,P,co-fork,fork,house,net)-free
(C₅,P,P₅,P,co-fork,fork,house)-free
(C₅,P₅,gem)-free
(C₅,S₃,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,3K₂,P₂ ∪ P₄,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-free
(C₅,S₃,3K₂,P₂ ∪ P₄)-free ∩ P₄-tidy
(C₅,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-free
(C₅,bull,co-gem,gem)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-free
C₅-free ∩ P₄-extendible
C₅-free ∩ P₄-tidy
C₅-free ∩ matrogenic
(C_n+4,P₅,bull)-free
(C_n+4,P₅,claw,gem)-free
(C_n+4,S₃,claw,net)-free
(C_n+4,X₁₀₂,X₂₀₄,P₃ ∪ 2K₁,gem)-free
(C_n+4,K₃ ∪ 3K₁,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
Delaunay
Dilworth 1
E-free ∩ planar
F_n grid
Gabriel
HHDG-free
H_n,q grid
(K₂ ∪ K₃,P₄,butterfly)-free
(K₂ ∪ K₃,P,X₁₆₃,X₉₅,co-diamond,house)-free
(K₂ ∪ claw,triangle)-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
(K_2,3,P₄,co-butterfly)-free
(K₃ ∪ 3K₁,C_n+4,co-dart,co-gem)-free
(K_3,3,K₅)-minor-free
(K₄,P₄)-free
(K₄,claw,diamond)-free
K₄-free ∩ map
K₄-free ∩ planar
(K₅ - e,S₃,3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
(K₅ - e,W₅,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-C₅,co-twin-house)-free
(K₅ - e,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
Laman ∩ planar
NLCT-width 1
(P,P₅,S₃,P,co-fork,fork,house,net)-free
(P,P₅,3K₂,gem)-free
(P,P₅,P,co-fork,fork,house)-free
(P,P₅,co-fork)-free
(P,P,co-fork,fork)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-gem,house)-free
(P₃ ∪ 2K₁,C_n+4,X₁₀₂,X₂₀₄,co-gem)-free
P₃-free
(P₄,2P₃)-free
(P₄,co-cycle)-free
(P₄,co-diamond,co-paw)-free
(P₄,diamond,paw)-free
P₄-extendible
P₄-extendible ∩ P₄-sparse
P₄-free
P₄-free ∩ starlike
P₄-lite
P₄-reducible
P₄-sparse
P₄-tidy
P₄-tidy ∩ (S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
P₄-tidy ∩ balanced
P₄-tidy ∩ hereditary clique-Helly ∩ perfect
P₄-tidy ∩ perfect
(P₅,S₃,anti-hole,co-domino,co-gem)-free
(P₅,P,gem)-free
(P₅,anti-hole,co-domino,co-gem)-free
(P₅,bull,co-fork)-free
(P₅,bull,house)-free
(P₅,bull)-free ∩ interval
(P₅,co-fork,house)-free
(P₅,diamond)-free
(P₅,fork,house)-free
(P₅,gem)-free
(P₅,triangle)-free
(P₆,triangle)-free
(S₃,3K₂,E,odd-hole)-free ∩ line
(S₃,claw,net)-free ∩ chordal
(S₃,net)-free ∩ extended P₄-sparse
Urquhart
(X₁₇₂,triangle)-free
(XC₁₁,claw,diamond)-free
(XC₁₂,triangle)-free ∩ planar
XC₉-free
(XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-free
(2C₄,3K₂,C₆,E,P₂ ∪ P₄,P₆,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,odd anti-cycle)-free
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,sunlet₄,odd anti-cycle)-free
(A,T₂,odd anti-cycle)-free
(C_n+4,bull,co-dart,co-gem)-free
(C_n+4,bull,house)-free
(C_n+4,co-claw,co-gem,house)-free
(C_n+4,co-claw,co-gem)-free
(C_n+4,co-dart,co-gem)-free
(C_n+4,co-diamond)-free
(C_n+4,co-gem)-free
(E,odd anti-cycle)-free
(P,butterfly,fork,gem)-free
(P,fork,gem)-free
(P,fork,house)-free
P₃-free
(P₇,star_1,2,3,sunlet₄,odd anti-cycle)-free
(P₇,star_1,2,3,odd anti-cycle)-free
(T₂,co-cycle)-free
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-free
(X₁₇₇,odd anti-cycle)-free
(XC₁₂,co-cycle)-free
(claw ∪ 3K₁,odd anti-cycle)-free
(star_1,2,3,sunlet₄,odd anti-cycle)-free
(star_1,2,3,odd anti-cycle)-free
(anti-hole,co-domino,odd anti-cycle)-free
astral triple-free
balanced ∩ line
bar visibility
block
block duplicate
book thickness 2
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
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,diamond,odd-hole)-free
(claw,diamond)-free
(claw,paw)-free
claw-free ∩ interval
clique graphs of interval
cliquewidth 2
cliquewidth 3
cliquewidth 4
cluster
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,house)-free
(co-fork,odd anti-cycle)-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
(co-paw,paw)-free
(co-paw,triangle)-free
co-probe cograph
co-probe threshold
co-trivially perfect
co-trivially perfect ∩ trivially perfect
cograph
cograph ∩ interval
cograph ∩ split
coin
comparability ∩ distance-hereditary
comparability graphs of arborescence orders
comparability graphs of series-parallel posets
comparability graphs of threshold orders
complete multipartite
complete split
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
disk contact
distance-hereditary
domination perfect ∩ planar
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
domishold
extended P₄-reducible
extended P₄-sparse
(fork,triangle)-free
genus 0
gridline
hamiltonian ∩ planar
hereditary clique-Helly ∩ line ∩ perfect
hole-free ∩ planar
homogeneously representable
homothetic triangle contact
indifference
intersection graph of nested intervals
line
line ∩ mock threshold
line ∩ perfect
line ∩ well covered
line graphs of acyclic multigraphs
line graphs of bipartite graphs
line graphs of planar cubic bipartite graphs
line graphs of triangle-free graphs
linear NLC-width 1
linear cliquewidth 2
linear domino
linear domino ∩ maximum degree 4
linear interval
linearly convex triangular grid graph
locally connected ∩ triangular grid graph
matrogenic
matroidal
maximal planar
maximum degree 3 ∩ planar ∩ triangle-free
minimally imperfect
odd-hole-free ∩ planar
partial bar visibility
partner-limited
perfect ∩ planar
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
probe P₄-reducible
probe P₄-sparse
probe bipartite distance-hereditary
probe block
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe complete
probe distance-hereditary
probe ptolemaic
probe threshold
probe threshold ∩ split
probe trivially perfect
proper interval
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-threshold
relative neighbourhood graph
restricted block duplicate
semi-P₄-sparse
semicircular
solid triangular grid graph
starlike threshold
strict B₁-VCPG
strictly chordal
strong tree-cograph
subhamiltonian
superfragile
thick tree
threshold
tree-cograph
triangle contact
triangular grid graph
trivially perfect
unit bar visibility
unit interval
weak bar visibility

GI-complete

NP-hard

NP-complete

(0,3)-colorable
(1,1)-colorable
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
(1,2)-split
1-DIR
(2,0)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
2-DIR
2-SEG
2-circular arc
2-circular track
2-interval
2-split
2-split ∩ perfect
2-subdivision
2-thin
2-track
(2K₂,A,C₅,2P₃,X₁₇₀,house)-free
(2K₂,C₄,C₅)-free
(2K₂,C₄)-free
(2K₂,C₅,C₆,C₇,C₈)-free
(2K₂,C₅,T₂)-free
(2K₂,C₅)-free
(2K₂,2P₃,C₆)-free
(2K₂,P₆)-free
(2K₂,house)-free
(2K₂,odd anti-hole)-free
2K₂-free
(2K₃ + e,5-pan,A,C₆,E,K_3,3-e,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,5-pan,A,C₆,E,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,antenna,co-antenna,co-domino,co-fish,co-twin-C₅,co-twin-house,domino,fish,twin-C₅,twin-house)-free
(2K₃ + e,A,C₅,C₆,E,K_3,3-e,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,A,C₆,E,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K₃ + e,X₉₈,house)-free
(2K₃ + e,X₉₉,house)-free
(2K₃ + e,house)-free
(2K₃,2K₃ + e,2P₃,C₅,C₆,C₇,K_2,3,K₃ ∪ P₃,W₄,X₈₄,X₉₅,A,C₆,P₆,X₅,X₉₈,butterfly,co-domino,co-fish,fish)-free
(2K₃,2K₃ + e,A,H,X₄₅,XZ₅,co-domino)-free
(2K₃,2P₃,C₅,C₆,C₇,K_2,3,K₃ ∪ P₃,X₈₄,3K₂,C₄ ∪ P₂,C₆,P₂ ∪ P₄,P₆,X₁₈,X₅,co-antenna,co-domino,co-fish)-free
(2K₃,2P₃,C_n+4,K₃ ∪ P₃)-free
(2K₃,C_n+4)-free
(2K₃,X₄₂,A,H,X₄₅,X₄₆,X₄₇,X₄₈,X₄₉,X₅₀,X₅₁,X₅₂,X₅₃,X₅₄,X₅₅,X₅₆,X₅₇)-free
(2K₃,house)-free
(2K₄,house)-free
(2P₃,3K₂,C₄ ∪ P₂,C₆,K_2,3,P₆,X₁₃₀,X₁₃₂,X₁₃₄,X₁₅₂,X₁₅₃,X₁₅₄,X₁₅₅,X₁₅₆,X₁₅₇,X₁₅₈,X₁₈,X₈₄,X₁₁,X₁₂₇,X₁₂₈,X₁₂₉,X₁₃₁,X₁₃₃,X₁₃₅,X₁₃₆,X₁₃₇,X₁₃₈,X₁₃₉,X₁₄₀,X₁₄₁,X₁₄₂,X₁₄₃,X₁₄₄,X₁₄₅,X₁₄₆,X₁₄₇,X₁₄₈,X₁₄₉,X₁₅₀,X₁₅₁,X₃₀,X₃₅,X₄₆,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺³,co-antenna,co-eiffeltower,co-longhorn,domino,fish,odd anti-hole)-free
(2P₃,C₄,C₅,P₅,X₁₇₀,A)-free
(2P₃,C₄,C₆)-free
2P₃-free
3-DIR
3-Helly
3-circular track
3-interval
3-mino
3-track
3K₁-free
(3K₂,C₄ ∪ P₂,C₅,C₆,K₂ ∪ K₃,K_3,3,K_3,3+e,P₂ ∪ P₄,P₆,X₁₈,X₅,2P₃,C₆,C₇,X₈₄,antenna,domino,fish)-free
(3K₂,C₅,C₇,P₂ ∪ P₄,X₁₇₃,X₁₁,net)-free
(3K₂,C₅,P₂ ∪ P₄,net)-free
(3K₂,E,P₂ ∪ P₄,net,odd anti-hole,odd-hole)-free
(3K₂,E,P₂ ∪ P₄,net)-free
(3K₂,E,net,odd anti-hole)-free
(3K₂,co-paw,odd anti-hole)-free
(3K₃,C_n+4)-free
(3P₃,C_n+4,P₃ ∪ P₄,P₅,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,A)-free
(3P₃,P₃ ∪ P₄,P₅,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,X₁₈₄,X₁₈₅,X₁₈₆,X₁₈₇,X₁₈₈,X₁₈₉,X₁₉₀,X₁₉₁,X₁₉₂,X₁₉₃,5-pan,A,P₆,co-twin-C₅)-free
(4,0)-colorable
4-colorable
(4-fan,K_1,4,W₄,W₅,A ∪ K₁,co-fork ∪ K₁,gem ∪ K₁,net ∪ K₁)-free
(4K₁,C₇,S₃,X₁₇₅,X₁₇₆,X₄₂,X₃₆,claw,co-antenna,net,odd anti-hole)-free
(4K₁,net)-free
(4K₁,odd anti-hole,odd-hole)-free
4K₁-free
(5,2)
(5,2)-chordal
(5,2)-odd-chordal
(5,2)-odd-noncrossing-chordal
5-colorable
(5-pan,A,P₆,X₁₈₆,3P₃,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,X₁₈₄,X₁₈₅,X₁₈₇,X₁₈₈,X₁₈₉,X₁₉₀,X₁₉₁,X₁₉₂,X₁₉₃,house,twin-C₅)-free
(5-pan,T₂,X₁₇₂)-free
5K₁-free
(6,1)-chordal
(6,1)-even-chordal
(6,2)-chordal
6-colorable
(6-fan,C₄ ∪ P₂,C₅,C₆ ∪ K₁,C₇,K₂ ∪ K₃,K_2,3,P₂ ∪ P₄,W₄ ∪ K₁,W₆,X₁₃₂,X₁₆₉,X₁₇₆,X₁₈,X₁₉₇,X₁₉₈,X₁₉₉,X₂₀₀,X₂₀₁,X₂₀₂,X₃₅,X₈₄,C₄ ∪ P₂,C₆ ∪ K₁,C₇,P₂ ∪ P₄,W₄ ∪ K₁,W₆,X₁₃₂,X₁₆₉,X₁₇₆,X₁₈,X₁₉₇,X₁₉₈,X₁₉₉,X₂₀₀,X₂₀₁,X₃₅,X₈₄,butterfly ∪ K₁,butterfly ∪ K₁,co-6-fan,co-fish,fish)-free
6K₁-free
7K₁-free
(A,C₅,C₆,K₂ ∪ K₃,K_3,3,K_3,3+e,K_3,3-e,P₆,X₅,X₉₈,2P₃,C₆,C₇,W₄,X₈₄,X₉₅,co-butterfly,co-fish,domino,fish)-free
(A,C₅,C₆,P₆,domino,house)-free
(A,C₅,P₅,A,house,parachute,parapluie)-free
(A,H,K_3,3,K_3,3-e,X₄₅,XZ₅,domino)-free
(A,H,K_3,3,X₄₅,X₄₆,X₄₇,X₄₈,X₄₉,X₅₀,X₅₁,X₅₂,X₅₃,X₅₄,X₅₅,X₅₆,X₅₇,X₄₂)-free
(A,H,K_3,3,X₄₅,triangle)-free
(A,P₆,domino)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AT-free
AT-free ∩ chordal
AT-free ∩ claw-free
B₀-VPG
B₀-VPG ∩ chordal
B₀-VPG ∩ strongly chordal
B₁-VPG
B₂-VPG
B₃-VPG
(BW₃,W₅,W₇,X₁₀₃,X₁₀₄,X₁₀₅,X₁₀₆,X₁₀₇,X₁₀₈,X₁₀₉,X₁₁₀,X₁₁₁,X₁₁₂,X₁₁₃,X₁₁₄,X₁₁₅,X₁₁₆,X₁₁₇,X₁₁₈,X₁₁₉,X₁₂₀,X₁₂₁,X₁₂₂,X₁₂₃,X₁₂₄,X₁₂₅,X₁₂₆,X₅₃,X₈₈,C₆,C₈,T₂,X₃)-free
BW₃-free
Berge
Berge ∩ bull-free
Berge ∩ claw-free
B_k-VPG
Bouchet
(C₄ ∪ P₂,C₅,C₆,K₂ ∪ K₃,K_2,3,P₆,W₄,X₁₈,X₅,X₈₄,C₄ ∪ P₂,C₆,P₆,W₄,X₁₈,X₅,X₈₄,antenna,co-antenna,co-domino,co-fish,domino,fish)-free
(C₄,C₅,C₆,C₇,C₈,H,X₈₅,triangle)-free
(C₄,C₅,C₆,C₇,C₈)-free
(C₄,C₅,C₆,S₃)-free
(C₄,C₅,K₄,diamond)-free
(C₄,C₅,T₂)-free
(C₄,C₅)-free
(C₄,C₅)-free ∩ Helly
(C₄,C₅)-free ∩ cop-win
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,S₃)-free
(C₄,A,H)-free
(C₄,co-claw)-free
(C₄,diamond)-free
(C₄,odd-hole)-free
(C₄,triangle)-free
C₄-free
C₄-free ∩ co-comparability
C₄-free ∩ induced-hereditary pseudo-modular
C₄-free ∩ odd-signable
C₄-free ∩ perfect
(C₅,C₆,P₆,X₁₇,X₁₈,X₅,X₉₈,C₆,P₆,antenna,domino)-free
(C₅,C₆,P₆,C₆,P₆,X₁₇,X₁₈,X₅,X₉₈,co-antenna,co-domino)-free
(C₅,C₆,P₆,C₆,P₆)-free
(C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄,triangle)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,house)-free
(C₅,P,P,bull,co-fork,gem,house)-free
(C₅,P₂ ∪ P₃,house)-free
(C₅,P₅,A,C₆,P₆,co-domino)-free
(C₅,P₅,P,house)-free
(C₅,P₅,P₂ ∪ P₃)-free
(C₅,P₅,co-fish,fish,house)-free
(C₅,P₅,house)-free
(C₅,P₅)-free
(C₅,P₆,P₆)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free
(C₅,S₃,3K₂,P₂ ∪ P₄)-free
(C₅,house)-free
C₅-free
(C₆,C₈,T₂,X₃,BW₃,W₅,W₇,X₁₀₃,X₁₀₅,X₁₀₆,X₁₀₇,X₁₀₈,X₁₀₉,X₁₁₀,X₁₁₁,X₁₁₂,X₁₁₃,X₁₁₄,X₁₁₅,X₁₁₆,X₁₁₇,X₁₁₈,X₁₁₉,X₁₂₀,X₁₂₁,X₁₂₂,X₁₂₃,X₁₂₄,X₁₂₅,X₁₂₆,X₅₃,X₈₈,co-X₁₀₄)-free
(C₆,K_3,3+e,P,P₇,X₃₇,X₄₁)-free
(C₆,P₆,P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,anti-hole,co-antenna)-free
(C₆,C₆)-free
(C₆,C₆)-free murky
(C₆,house)-free
(C₆,triangle)-free
C₆-free
(C₇,odd anti-hole)-free
CONV
(C_n+4 ∪ K₁,K_2,3,T₂,W_n+4,X₃₁,XF₂ⁿ⁺¹,XF₃ⁿ,C₆,X₃₇,X₉₀,domino,twin-C₅)-free
(C_n+4,S₃,net)-free
(C_n+4,S₃)-free
(C_n+4,T₂,X₃₁,XF₂ⁿ⁺¹,XF₃ⁿ)-free
(C_n+4,T₂,XF₂ⁿ⁺¹)-free
(C_n+4,T₂,net)-free
(C_n+4,X₅₉,longhorn)-free
(C_n+4,odd-sun)-free
(C_n+4,sun)-free
C_n+4-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,X₃₇,X₃₈,X₃₉,X₄₀,X₄₁,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,anti-hole,co-XF₁²ⁿ⁺³,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,co-XF₁²ⁿ⁺³,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd anti-hole)-free
(C_n+6,X₃₇,claw,co-antenna,net,sun)-free
C_n+6-free
C_n+7-free
(E,P)-free
E-free
EPT
EPT ∩ chordal
Gallai
Gallai-perfect
(H,triangle)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDS-free
HHDbicycle-free
HHP-free
Hamiltonian hereditary
Helly
Helly 2-acyclic subtree
Helly ∩ bridged
Helly cactus subtree
Helly cactus subtree ∩ perfect
Helly chordal
Helly chordal ∩ clique-chordal
Helly circular arc
Helly circular arc ∩ (C₇,odd-hole)-free
Helly circular arc ∩ perfect
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
K_1,4-free
(K₂ ∪ K₃,X₁₁,X₁₂₇,X₁₂₈,X₁₂₉,X₁₃₁,X₁₃₃,X₁₃₅,X₁₃₆,X₁₃₇,X₁₃₈,X₁₃₉,X₁₄₀,X₁₄₁,X₁₄₂,X₁₄₃,X₁₄₄,X₁₄₅,X₁₄₆,X₁₄₇,X₁₄₈,X₁₄₉,X₁₅₀,X₁₅₁,X₃₀,X₃₅,X₄₆,XF₁²ⁿ⁺³,XF₆²ⁿ⁺³,2P₃,3K₂,C₄ ∪ P₂,C₆,P₆,X₁₃₀,X₁₃₂,X₁₃₄,X₁₅₂,X₁₅₃,X₁₅₄,X₁₅₅,X₁₅₆,X₁₅₇,X₁₅₈,X₁₈,X₈₄,antenna,co-domino,co-fish,eiffeltower,longhorn,odd-hole)-free
(K₂ ∪ K₃,P,anti-hole)-free
(K₂ ∪ K₃,P,house)-free
(K₂ ∪ K₃,house)-free
K₂ ∪ K₃-free
K₂ ∪ claw-free
(K_2,3,P,P₅)-free
(K_2,3,P,hole)-free
(K_2,3,P₅)-free
(K_2,3,X₃₇,X₃₈,diamond,domino,house,twin-C₅)-free
(K_2,3,diamond)-free
K_2,3-free
(K₃ ∪ 2K₁,K₃ ∪ 2K₁,bull,co-cricket,co-dart,cricket,dart)-free
(K₃ ∪ P₃,C₆,P,P₇,X₃₇,X₄₁)-free
(K_3,3,3,C_n+4)-free
(K_3,3,K_3,3+e,2P₃,C_n+4)-free
(K_3,3,P₅)-free
(K_3,3,C_n+4)-free
(K_3,3-e,P₅,X₉₈)-free
(K_3,3-e,P₅,X₉₉)-free
(K_3,3-e,P₅)-free
(K_4,4,P₅)-free
(K₄,S₃)-free
K₄-free
K₅-free
K₆-free
K₇-free
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
(P,P₅)-free
(P,P₇)-free
(P,P₈)-free
(P,T₂)-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
(P₂ ∪ P₃,P₃ ∪ 2K₁,X₁₈₈,X₂₁₄,W₄,X₁₀₂,X₂₀₄,X₂₀₉,X₂₁₀,X₂₁₂,X₂₁₃,X₂₁₅,X₂₁₆,X₂₁₇,X₂₁₈,X₈₆,co-gem)-free
(P₂ ∪ P₃,house)-free
P₂ ∪ P₄-free
P₄-bipartite
P₄-brittle
P₄-laden
P₄-simplicial
(P₅,X₈₂,X₈₃)-free
(P₅,A,anti-hole,co-domino)-free
(P₅,C₆)-free
(P₅,C₆)-free ∩ weakly chordal
(P₅,P,anti-hole)-free
(P₅,P₂ ∪ P₃)-free
(P₅,X₃₈,co-gem)-free
(P₅,anti-hole,co-bicycle,co-domino)-free
(P₅,anti-hole,co-domino)-free
(P₅,anti-hole)-free
(P₅,bull,odd anti-hole)-free
(P₅,bull)-free
(P₅,claw)-free
(P₅,cricket)-free
(P₅,fork)-free
(P₅,house)-free
P₅-free
P₅-free ∩ weakly chordal
(P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,C₆,P₆,antenna,hole)-free
(P₆,X₃₀,X₈)-free
(P₆,claw)-free
P₆-free
P₇-free
PI
PI^*
(S₃,S₄,net)-free
(S₃,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,X₄₂)-free
(S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
(S₃,3K₂,E,P₂ ∪ P₄)-free
(S₃,3K₂,E,odd-hole)-free
(S₃,C_n+6,X₃₇,antenna,co-claw,co-sun)-free
(S₃,claw,net)-free
(S₃,co-claw,net)-free
(S₃,co-claw)-free
(S₃,net)-free
(S₃,net)-free ∩ chordal
(S₃,net)-free ∩ sun-free
S₃-free
S₃-free ∩ chordal
SEG
V-perfect
VPG
W_2n+3-free
(W₄,W₅,butterfly)-free
(W₄,X₁₀₂,X₂₀₄,X₂₀₉,X₂₁₀,X₂₁₂,X₂₁₃,X₂₁₄,X₂₁₅,X₂₁₆,X₂₁₇,X₂₁₈,X₈₆,P₂ ∪ P₃,P₃ ∪ 2K₁,X₁₈₈,gem)-free
(W₄,gem)-free
Welsh-Powell opposition
Welsh-Powell perfect
W_n+4-free
(X₁₂,X₅,X₉₅,X₉₆,X₉₇,X₁₂,X₅,X₉₅,X₉₆,X₉₇,claw ∪ triangle,claw ∪ triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free
(X₃₀,XZ₁,XZ₄,longhorn)-free
(X₃₈,gem,house)-free
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free
(X₇₉,X₈₀)-free
(X₉₁,claw)-free
XC₁₀-free
XC₁₃-free
β-perfect
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
cal C(G)-perfect
2P₃-free
(5-pan,T₂,X₁₇₂)-free
(A,P₆,co-domino)-free
BW₃-free
C₆-free
(C₇,odd-hole)-free
(C_n+4,X₅₉,co-longhorn)-free
C_n+4-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,X₃₇,X₃₈,X₃₉,X₄₀,X₄₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ)-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
K₂ ∪ claw-free
(P,P₇)-free
(P,P₈)-free
(P,T₂)-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
P₂ ∪ P₄-free
(P₆,X₃₀,X₈)-free
(P₆,co-claw)-free
P₆-free
P₇-free
W_2n+3-free
(W₄,W₅,co-butterfly)-free
(W₄,co-gem)-free
W_n+4-free
(X₃₀,XZ₁,XZ₄,co-longhorn)-free
(X₇₉,X₈₀)-free
(X₈₂,X₈₃,house)-free
(X₉₁,co-claw)-free
(n+4)-pan-free
odd-cycle ∪ K₁-free
τ_k-perfect for all k >= 2
absolutely perfect
absorbantly perfect
all-4-simplicial
almost claw-free
almost-split
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
alternation
(anti-hole,co-sun,hole)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd-hole)-free
anti-hole-free
apex
b-perfect
b-perfect ∩ chordal
balanced
balanced 2-interval
balanced ∩ chordal
basic perfect
biclique separable
biclique-Helly
bip^*
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
bitolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 1
boxicity 2
bridged
bridged ∩ clique-Helly
brittle
building-free
building-free ∩ even-signable
building-free ∩ odd-signable
(bull,co-fork)-free
(bull,fork)-free
(bull,hole,odd anti-hole)-free
(bull,house)-free
(bull,odd anti-hole,odd-hole)-free
bull-free
bull-free ∩ perfect
(butterfly,gem)-free
caterpillar arboricity <= 2
charming
chordal
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ co-comparability
chordal ∩ diametral path
chordal ∩ dually chordal
chordal ∩ hereditary clique-Helly
chordal ∩ hereditary dominating pair
chordal ∩ irredundance perfect
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular arc
circular arc ∩ clique-Helly
circular arc ∩ perfect
circular perfect
circular strip
circular trapezoid
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ perfect
clique graphs
clique separable
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
clique-perfect
co-Gallai
co-HHD-free
co-Matula perfect
co-Meyniel
co-P₄-brittle
co-Welsh-Powell opposition
co-Welsh-Powell perfect
co-β-perfect
co-biclique separable
co-bipartite
co-building-free
(co-butterfly,co-claw)-free
(co-butterfly,co-gem)-free
co-chordal
co-circular perfect
(co-claw,house)-free
(co-claw,odd anti-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 d
(co-cricket,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-domino-free
(co-fork,house)-free
co-fork-free
co-gem-free
co-hereditary clique-Helly
co-interval ∪ interval
co-interval filament
co-interval mixed
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-sun-free
co-threshold tolerance
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
cop-win
cubic
cycle-bicolorable
d-trapezoid
diametral path
diamond-free
directed path
disk
disk-Helly
dismantlable
domination
domination perfect
domination perfect ∩ triangle-free
(domino,gem,house)-free
domino-free
doubled
doubly chordal
dually chordal
even anti-cycle-free
even anti-hole-free
even-cycle-free
even-hole-free
even-hole-free ∩ probe chordal
even-signable
extended P₄-laden
fork-free
gem-free
generalized split
generalized strongly chordal
girth>=9
good
grid intersection
hereditary Helly
hereditary Matula perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary biclique-Helly
hereditary clique-Helly
hereditary disk-Helly
hereditary dismantlable
hereditary dominating pair
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary sat
hereditary weakly modular
(hole,odd anti-hole)-free
hole-free
homogeneously orderable
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
induced-hereditary pseudo-modular
intersection graphs of parallelograms (squares)
interval
interval filament
irredundance perfect
irredundance perfect with ir(G)<= 4
isometric-HH-free
isometric-hereditary pseudo-modular
k-DIR
k-SEG
kernel solvable
leaf power
leaf power ∪ min leaf power
line graphs of Helly hypergraphs of rank 3
linear arboricity <= 2
locally bipartite
locally chordal
locally perfect
locally split
max-tolerance
maxibrittle
maximal clique irreducible
maximum degree 3
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
monopolar
multitolerance
murky
(n+4)-pan-free
nK₂-free, fixed n
nP₃-free, fixed n
neighbourhood chordal
neighbourhood perfect
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
net-free
normal
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
odd anti-hole-free
(odd building,odd-hole)-free
odd co-sun-free
odd-hole-free
odd-hole-free ∩ pretty
odd-signable
odd-sun-free
open-neighbourhood-Helly
opposition
outer-string
(p,q<=2)-colorable
p-connected
pairwise compatibility
parallelepiped
partial rectangle visibility
path orderable
paw-free
perfect
perfect ∩ split-neighbourhood
perfect cochromatic
perfect connected-dominant
perfectly 1-transversable
perfectly contractile
perfectly orderable
polar
power-chordal
preperfect
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe AT-free
probe Gallai
probe HHDS-free
probe Meyniel
probe chordal
probe chordal ∩ weakly chordal
probe co-bipartite
probe co-comparability
probe diamond-free
probe interval
probe split
probe strongly chordal
pseudo-modular
pseudo-split
quasi-Meyniel
quasi-brittle
quasi-line
quasi-parity
quasitriangulated
rectangle intersection
rectangle visibility
rigid circuit
rooted directed path
semi-square intersection
semiperfectly orderable
short-chorded
slender
slightly triangulated
slim
spider graph
split
split-neighbourhood
split-perfect
starlike
strict quasi-parity
strictly clique irreducible
string
strong asteroid free
strong domination perfect
strongly chordal
strongly circular perfect
strongly even-signable
strongly orderable
strongly perfect
substar
subtree filament
subtree overlap
sun-free
sun-free ∩ weakly chordal
superbrittle
thickness <= 2
tolerance
totally unimodular
trapezoepiped
trapezoid
triangle-free
triangulated
tripartite
undirected path
unimodular
unipolar
unit 2-circular track
unit 2-track
unit 3-circular track
unit 3-track
unit disk
universally signable
upper domination perfect
upper irredundance perfect
very strongly perfect
weak bipolarizable
weak bisplit
weak dominating pair
weak rectangle visibility
weakly chordal
weakly geodetic
weakly modular
well-partitioned chordal

coNP-complete

Open

Unknown to ISGCI

(0,2)-graph
1-bounded tripartite
1-string
(2,2)-interval
2-connected
2-connected ∩ (4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
2-connected ∩ (P₆,claw)-free
2-edge-connected
2-strongly regular
2-threshold
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈)-free
(2K₂,3K₁)-free
(2K₂,4K₁,C₅,co-diamond)-free
(2K₂,4K₁,co-claw,co-diamond)-free
(2K₂,5K₁,C₅,K₃ ∪ 2K₁,P₃ ∪ 2K₁,C₆,C₇,C₈,K_1,4,K₅ - e,claw ∪ K₁,co-butterfly,co-cricket,co-dart,co-gem)-free
(2K₂,A,H)-free
(2K₂,C₄,C₅,S₃,co-rising sun,net,rising sun)-free
(2K₂,C₄,C₅,S₃,co-rising sun,net)-free
(2K₂,C₄,C₅,S₃,net,rising sun)-free
(2K₂,C₄,C₅,S₃,net)-free
(2K₂,C₄,C₅,co-sun)-free
(2K₂,C₄,C₅,sun)-free
(2K₂,C₅,C₆,C₇,C₈,XC₁₁,co-claw,co-diamond)-free
(2K₂,C₅,C₆,net)-free
(2K₂,C₆,C₈,K_1,4,odd anti-cycle)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,X₉₁,co-claw)-free
(2K₂,claw)-free
(2K₂,co-claw,co-diamond)-free
(2K₂,co-diamond)-free
(2K₂,net)-free
(2K₃ + e,3K₁,C₅,T₂,X₁₈,X₉₄,co-domino)-free
(2K₃ + e,A,C₅,C₆,E,H,K_3,3-e,R,X₁₆₈,X₁₇₁,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,A,C₆,E,H,R,X₁₆₈,X₁₇₁,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,antenna,co-antenna,co-domino,co-fish,co-twin-house,domino,fish,twin-house)-free
(2K₃ + e,C₅,C₆,P₆,X₅,2P₄,A,C₆,C₇,E,P₇,R,X₁,X₁₀₃,X₅,X₅₈,X₈₄,X₉₈,antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet₄)-free
(2K₃,2K₃ + e,3K₁,A,H,T₂,X₁₈,X₄₅,co-domino)-free
(2K₃,3K₁,A,H,X₄₅)-free
(2P₃,triangle)-free
(2P₄,A,C₅,C₆,C₇,E,K_3,3-e,P₇,R,X₁,X₁₀₃,X₅,X₅₈,X₈₄,X₉₈,C₆,P₆,X₅,sunlet₄,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
3-DIR contact
(3K₁,C₅,K₃ ∪ K₄,BW₃,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃)-free
(3K₁,C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄)-free
(3K₁,2P₃)-free
(3K₁,3K₂)-free
(3K₁,C₆)-free
(3K₁,E)-free
(3K₁,H)-free
(3K₁,K_1,5)-free
(3K₁,P₂ ∪ P₄)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,XC₁₂)-free
(3K₁,co-cross)-free
(3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,K₅ - e,co-claw,net,odd anti-hole,twin-house)-free
(3K₂,C₄ ∪ P₂,C₅,P₂ ∪ P₄,P₅,S₃,X₁,X₄₆,X₇₀,3K₂,C₄ ∪ P₂,P₂ ∪ P₄,X₁,X₄₆,X₇₀,co-fish,co-rising sun,fish,house,net,rising sun)-free
(3K₂,triangle)-free
(4-fan,C_n+4,K₅ - e,S₃,X₁₀₀,X₁₀₁,X₁₀₂,H,K₃ ∪ 2K₁)-free
(4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
4-regular
4-regular ∩ hamiltonian
(4K₁,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,house)-free
(4K₁,C₇,X₃₈,X₃₉,K_3,3 ∪ K₁,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,butterfly ∪ K₁,diamond)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,gem)-free
(4K₁,house)-free
(5,2)-odd-crossing-chordal
5-regular
5-regular ∩ hamiltonian
(6,3)
(7,5)
(A ∪ K₁,K_1,4,W₄,W₅,co-4-fan,co-fork ∪ K₁,gem ∪ K₁,net ∪ K₁)-free
(A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,K₅ - e,W₅,co-claw,twin-C₅,twin-house)-free
(A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,K₅ - e,co-claw,odd anti-hole,twin-house)-free
(A,E,S₃,X₁,domino,hole,house,net,rising sun)-free
(A,H,K_3,3,K_3,3-e,T₂,X₁₈,X₄₅,domino,triangle)-free
(A,P₆,clique wheel,domino,hole,house)-free
B₀-CPG
B₀-VPG ∩ triangle-free
B₁-CPG
B₁-VCPG
(BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-free
Birkhoff
(C₄,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅,triangle)-free
(C₄,C₅,C₆,C₇,C₈,H,X₈₅,triangle)-free ∩ K_1,4-free
(C₄,C₅,C₆,C₇,C₈,K_1,4,K₅,K₅ - e,K₃ ∪ 2K₁,P₃ ∪ 2K₁,claw ∪ K₁,butterfly,cricket,dart,gem)-free
(C₄,X₉₁,claw)-free
(C₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,gem,house)-free
(C₅,K_3,3-e,T₂,X₁₈,X₉₄,domino,triangle)-free
(C₅,P,P₅,P,bull,co-gem,fork)-free
(C₅,P,co-fork,fork,gem,house)-free
(C₅,P₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,co-gem)-free
(C₅,P₅,P,co-fork,co-gem,fork)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free ∩ co-line
(C₆,K₂ ∪ K₃,X₁₀₃,X₃₇,X₈₈,X₉₀,C_n+4 ∪ K₁,T₂,net ∪ K₁,co-diamond,co-domino,co-eiffeltower,co-twin-C₅)-free
(C₆,K₂ ∪ K₃,X₃₇,X₉₀,C_n+4 ∪ K₁,T₂,W_n+4,X₃₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-domino,co-twin-C₅)-free
(C₆,S₃,C_n+4 ∪ K₁,W₄,W₅,co-claw,net)-free
CIS
CPG
(C_n+3 ∪ K₁,diamond,paw)-free
(C_n+4 ∪ K₁,C(n,k),W₄,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,C(n,k),X₄₂,T₂,X₂,X₃,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,K_2,3,T₂,C₆,X₁₀₃,X₃₇,X₈₈,X₉₀,diamond,domino,eiffeltower,net ∪ K₁,twin-C₅)-free
(C_n+4 ∪ K₁,K_2,3,T₂,X₉₀,domino,paw,twin-C₅)-free
(C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,T₂,X₂,X₃,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4 ∪ K₁,S₃,W₄,W₅,C₆,claw,net)-free
(C_n+4 ∪ K₁,S₃,W₄,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4,H)-free
(C_n+4,S₃ ∪ K₁,X₁₀₃,claw,eiffeltower,net ∪ K₁)-free
(C_n+4,S₃ ∪ K₁,claw,net)-free
(C_n+4,XF₁²ⁿ⁺³,XF₆²ⁿ⁺²,X₃₄,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,claw,net)-free
(C_n+4,claw)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,XF₁²ⁿ⁺³,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,co-XF₁²ⁿ⁺³,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd anti-hole)-free
(C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,XF₁²ⁿ⁺³,XF₂ⁿ⁺¹,XF₃ⁿ,XF₄ⁿ,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₆,co-XF₁²ⁿ⁺³,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,co-XF₅²ⁿ⁺³,co-XF₆²ⁿ⁺²,odd-hole)-free
D
Deza
Dilworth 2
Dilworth 3
Dilworth 4
(E,triangle)-free
(H,K₃ ∪ 2K₁,C_n+4,K₅ - e,X₁₀₀,X₁₀₁,X₁₀₂,co-4-fan,net)-free
(H,K₃ ∪ 2K₁,C_n+4,K₅ - e,co-4-fan,net)-free
HHG-free
Hamilton-connected
Hamming
Helly ∩ reflexive
Helly circle
Helly circular arc ∩ concave-round
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
Helly subtree
(K_1,4,diamond)-free
(K_1,4,paw)-free
K_1,4-free ∩ almost claw-free ∩ locally connected
K_1,4-free ∩ well covered
(K_1,5,triangle)-free
(K₂ ∪ K₃,P₅,X₃₇,X₃₈,co-diamond,co-domino,co-twin-C₅)-free
(K₂ ∪ K₃,X₉₀,C_n+4 ∪ K₁,T₂,co-domino,co-paw,co-twin-C₅)-free
(K₂ ∪ K₃,co-diamond)-free
(K_2,3,diamond)-free ∩ weakly modular
(K_3,3 ∪ K₁,K₄,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,C₇,X₃₈,X₃₉,butterfly ∪ K₁,co-diamond)-free
(K₄,P₅,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉)-free
(K₄,P₅)-free
(K₄,S₃,X₃₆,C₇,X₁₇₅,X₁₇₆,X₄₂,antenna,co-claw,net,odd-hole)-free
(K₄,co-gem)-free
(K₄,odd anti-hole,odd-hole)-free
(K₄,odd anti-hole,odd-hole)-free ∩ dually chordal
K₄-free ∩ dually chordal ∩ perfect
K₄-free ∩ perfect
Laman
Mycielski
N^*
N^*-perfect
(P₂ ∪ P₄,triangle)-free
P₄-comparability
P₄-indifference
(P₅,S₃,A,E,X₁,anti-hole,co-domino,co-rising sun,net)-free
(P₅,A,P₆,anti clique wheel,anti-hole,co-domino)-free
(P₅,anti-hole,co-domino,co-sun)-free
(P₅,anti-hole,co-gem)-free
(P₅,co-domino,co-gem)-free
(P₅,co-fork)-free
P₅-free ∩ tripartite
P₆-free ∩ tripartite
PURE-3-DIR
PURE-k-DIR
Raspail
(S₃,T₂,X₂,X₃,C_n+4 ∪ K₁,C(n,k),X₄₂,even-hole,odd-cycle ∪ K₁)-free
(S₃,T₂,X₂,X₃,C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,even-hole,odd-cycle ∪ K₁)-free
(S₃,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,C_n+4 ∪ K₁,S₃ ∪ K₁,X₄₂,even-hole,odd-cycle ∪ K₁)-free
(S₃,C_n+4 ∪ K₁,C(n,k),W₄,even-hole,odd-cycle ∪ K₁)-free
(S₃,C_n+4,S₃ ∪ K₁,co-claw)-free
(S₃,C_n+4,T₂)-free
(S₃,C_n+4,co-claw,net)-free
(S₃,C_n+4,co-claw)-free
(S₃,C_n+4,net)-free
(S₃,net)-free ∩ split
(W₄,claw,gem,odd-hole)-free
(W₄,claw,gem)-free
(W₄,claw)-free
(W₄,gem)-free ∩ short-chorded
(X₁₀₃,C_n+4,S₃ ∪ K₁,net ∪ K₁,co-claw,co-eiffeltower)-free
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₃₇,diamond,even-cycle)-free
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free ∩ normal circular arc ∩ quasi-line
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
XC₁₀-free ∩ pseudo-modular
XC₁₀-free ∩ weakly modular
(XC₁₂,triangle)-free
(XC₇,XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₈)-free
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,hole)-free
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,odd-hole)-free
cal P₃-perfect
(3K₂,odd-hole,paw)-free
(C_n+3 ∪ K₁,co-diamond,co-paw)-free
(C_n+4,H)-free
(C_n+4,T₂,X₃₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,T₂,co-XF₂ⁿ⁺¹)-free
(C_n+4,co-claw)-free
(C_n+4,co-sun)-free
(C_n+4,net)-free
(C_n+4,odd co-sun)-free
(C_n+6,odd anti-cycle)-free
(K_1,4,co-diamond)-free
(K_1,4,co-paw)-free
(K_1,4,odd anti-cycle)-free
(P,fork)-free
(P₇,odd anti-cycle)-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even anti-hole,odd anti-cycle)-free
(W₄,co-claw,co-gem,odd anti-hole)-free
(W₄,co-claw,co-gem)-free
(W₄,co-claw)-free
(X₃₇,co-diamond,even anti-cycle)-free
XC₁₀-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
XC₁₁-free
XC₁₂-free
XC₁₃-free
absolute reflexive retract
almost CIS
(anti-hole,bull,odd-hole)-free
(anti-hole,fork)-free
(anti-hole,odd anti-cycle)-free
balanced ∩ co-line
balanced ∩ paw-free
basic 4-leaf power
bigeodetic
bipartable
bipolarizable
bisplit
bithreshold
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded treewidth
boxicity 2 ∩ co-bipartite
(bull,house,odd-hole)-free
(butterfly,claw)-free
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ co-chordal ∩ co-comparability ∩ comparability
chordal ∩ comparability
chordal ∩ domination perfect
chordal ∩ hamiltonian
chordal ∩ proper circular arc
chordal-perfect
circle
circle ∩ diamond-free
circle graph with equator
circular arc ∩ co-bipartite
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular interval
circular permutation
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
claw-free ∩ locally connected
claw-free ∩ mock threshold
claw-free ∩ normal Helly circular arc
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ upper domination perfect
claw-free ∩ well covered
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
clique-Helly ∩ dismantlable ∩ reflexive
clique-perfect ∩ triangle-free
co-2-subdivision
co-biconvex
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bithreshold ∩ split
co-bounded tolerance
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,odd anti-hole,odd-hole)-free
(co-claw,odd-hole)-free
co-comparability ∩ comparability
co-comparability graphs of posets of interval dimension 2, height 2
(co-diamond,even anti-cycle)-free
co-forest-perfect
(co-fork,hole)-free
co-interval
co-interval ∩ interval
co-interval bigraph
co-interval containment bigraph
co-leaf power
co-line
co-line graphs of bipartite graphs
co-planar
co-proper interval bigraph
co-quasi-line
co-strongly chordal
co-tolerance
co-trapezoid
comparability
comparability ∩ split
comparability ∩ weakly chordal
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 3
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
complete Hamming
concave-round
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex-round
(cross,triangle)-free
cubic ∩ hamiltonian
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free ∩ perfect
distance regular
distance regular of diameter 2
domino
double split
dually chordal ∩ tripartite
edge regular
equimatchable
forest-perfect
(fork,house)-free
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
generically minimally rigid
genus 1
geodetic
graceful
hamiltonian
hamiltonian ∩ interval
hamiltonian ∩ split
harmonious
hereditary N^*-perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary clique-Helly ∩ self-clique
interval enumerable
interval regular
interval regular of diameter 2
irredundance perfect with ir(G)=2
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
leaf power ∩ min leaf power
line graphs of bipartite multigraphs
line graphs of linear hypergraphs of rank 3
line graphs of multigraphs without triangles
line perfect
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
map
middle
min leaf power
mock threshold
mock threshold ∩ split
module-composed
nearly bipartite
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
odd-cycle ∪ K₁-free
(odd-hole,paw)-free
odd-signable ∩ triangle-free
overlap
(p,q)-colorable
(p,q)-split
p-tree
parity
partitionable
paw-free ∩ perfect
perfectly colorable
permutation
permutation ∩ split
probe chordal bipartite
probe comparability
probe permutation
probe proper interval
probe unit interval
proper Helly circular arc
proper chordal
proper circular arc
proper tolerance
pseudo-median
(q,t)
quasi-median
rectagraph
reflexive
self-clique
self-complementary
skeletal
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
square of tree
strict 2-threshold
strongly 3-colorable
strongly odd-signable
strongly regular
superperfect
threshold signed
threshold tolerance
toroidal
tree-perfect
unbreakable
unigraph
unit 2-circular arc
unit 2-interval
unit 3-interval
unit Helly circle
unit Helly circular arc
unit circular arc
unit grid intersection
unit tolerance
visibility
walk regular
weakly median
well covered
well-dominated
wing-triangulated