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

Problem: Weighted feedback vertex set

Definition:

Input: A graph G in this class with weight function on the vertices and a real k.

Output: True iff G contains a set S of vertices, such that the sum of the weights of the vertices in S is at most k and 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
(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,H,S₃,X₁₆₀,X₁₅₉,net,rising sun)-free
(2K₂,C₄,C₅,S₃,X₁₅₉,X₁₆₀,H,co-rising sun,net)-free
(2K₂,C₄,C₅,S₃,claw,net)-free
(2K₂,C₄,C₅,S₃,co-claw,net)-free
(2K₂,C₄,C₅,S₃,co-rising sun,net,rising sun)-free
(2K₂,C₄,C₅,S₃,net,rising sun)-free
(2K₂,C₄,C₅,claw,diamond)-free
(2K₂,C₄,C₅,co-claw,co-diamond)-free
(2K₂,C₄,P₄,triangle)-free
(2K₂,C₄,P₄)-free
(2K₂,C₅,triangle)-free
(2K₂,K_3,3,K_3,3+e,P₄,2P₃)-free
(2K₂,P₃,triangle)-free
(2K₂,P₃)-free
(2K₂,P₄,2P₃)-free
(2K₂,P₄,co-dart)-free
(2K₂,P₄,co-diamond,co-paw)-free
(2K₂,P₄)-free
2K₂-free ∩ bipartite
(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,C₄,P₃)-free
(3K₁,C₅,butterfly,diamond)-free
(3K₁,P₃)-free
(3K₁,P₄)-free
(3K₁,P₃)-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
(4K₁,K₄)-free
(4K₁,P₄)-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 ∩ chordal
(C₄,P₄,dart)-free
(C₄,P₄,diamond,paw)-free
(C₄,P₄)-free
(C₄,P₃,triangle)-free
(C₄,P₃)-free
C₄-free ∩ co-comparability
(C₅,C₆,P₆,triangle)-free
(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,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,co-butterfly,co-diamond,triangle)-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,T₂,X₃₁,XF₂ⁿ⁺¹,XF₃ⁿ)-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
Dilworth 1
HHDG-free
(K₂ ∪ K₃,P₄,butterfly)-free
(K₂ ∪ K₃,P,X₁₆₃,X₉₅,co-diamond,house)-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
(K_2,3,P₄,co-butterfly)-free
K₂-free
K₃-minor-free
(K₄,P₄)-free
NLCT-width 1
(P,P₅,S₃,P,co-fork,fork,house,net)-free
(P,P₅,P,co-fork,fork,house)-free
(P,P,co-fork,fork)-free
(P₃,triangle)-free
P₃-free
(P₄,2P₃)-free
(P₄,co-cycle)-free
(P₄,co-diamond,co-paw)-free
(P₄,cycle)-free
(P₄,diamond,paw)-free
(P₄,triangle)-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,bull,house)-free
(P₅,bull)-free ∩ interval
(P₅,co-fork,house)-free
(P₅,diamond)-free
(P₅,fork,house)-free
(P₅,triangle)-free
P₆-free ∩ chordal bipartite
(P₇,odd-cycle,star_1,2,3,sunlet₄)-free
(P₇,odd-cycle,star_1,2,3)-free
(S₃,claw,net)-free ∩ chordal
(S₃,net)-free ∩ extended P₄-sparse
(T₂,cycle)-free
(T₃,X₈₁,cycle)-free
(T₃,cycle)-free
(XC₁₂,cycle)-free
XC₉-free
(XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-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
(P₃,triangle)-free
P₃-free
astral triple-free
bi-cograph
binary tree
binary tree ∩ partial grid
bipartite ∩ bithreshold
bipartite ∩ bridged
bipartite ∩ claw-free
bipartite ∩ distance-hereditary
bipartite ∩ module-composed
bipartite chain
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 P₄-reducible
extended P₄-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
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-threshold
restricted block duplicate
semi-P₄-sparse
semicircular
split ∩ threshold signed
starlike threshold
strictly chordal
superfragile
thick tree
threshold
tolerance ∩ tree
tree
trivially perfect
unit interval

Polynomial

(0,3)-colorable ∩ chordal
(1,1)-colorable
(2,0)-colorable
2-bounded bipartite
2-outerplanar
2-terminal series-parallel
2-tree
2-tree ∩ probe interval
(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,C₅,2P₃,X₁₇₀,house)-free
(2K₂,A,H)-free
(2K₂,C₄,C₅,S₃,co-rising sun,net)-free
(2K₂,C₄,C₅,S₃,net)-free
(2K₂,C₄,C₅,co-sun)-free
(2K₂,C₄,C₅,sun)-free
(2K₂,C₄,C₅)-free
(2K₂,C₄)-free
(2K₂,C₅,S₃,X₁₅₉,X₁₆₀,X₁₆₁,X₁₆₂,X₄₆,X₇₀,2P₃,3K₂,H,P₂ ∪ P₄,X₁,co-rising sun,house,net)-free
(2K₂,C₅,C₆,C₇,C₈,XC₁₁,co-claw,co-diamond)-free
(2K₂,C₅,C₆,C₇,C₈)-free
(2K₂,C₅,C₆,net)-free
(2K₂,C₅,T₂)-free
(2K₂,C₅)-free
(2K₂,2P₃,C₆)-free
(2K₂,C₆,C₈,K_1,4,odd anti-cycle)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,P₆)-free
(2K₂,X₉₁,co-claw)-free
(2K₂,claw)-free
(2K₂,co-claw,co-diamond)-free
(2K₂,co-diamond)-free
(2K₂,house)-free
(2K₂,net)-free
(2K₂,odd anti-hole)-free
2K₂-free
2K₂-free ∩ probe cograph
2K₂-free ∩ probe trivially perfect
(2K₃ + e,3K₁,C₅,T₂,X₁₈,X₉₄,co-domino)-free
(2K₃,2K₃ + e,3K₁,A,H,T₂,X₁₈,X₄₅,co-domino)-free
(2K₃,3K₁,A,H,X₄₅)-free
3-tree
3-tree ∩ planar
(3K₁,C₅,K₃ ∪ K₄,BW₃,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃)-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,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,K₂ ∪ claw)-free
(3K₁,P₂ ∪ P₄)-free
(3K₁,P₆)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,X₁₇₂)-free
(3K₁,XC₁₂)-free
(3K₁,co-cross)-free
3K₁-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,C₆,P₇,X₁₆₄,X₁₆₅,odd-cycle,sunlet₄)-free
(3K₂,P,co-gem,house)-free
(4,0)-colorable
4-leaf power
(4K₁,C₇,S₃,X₁₇₅,X₁₇₆,X₄₂,X₃₆,claw,co-antenna,net,odd anti-hole)-free
(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,C_n+4)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,gem)-free
(4K₁,house)-free
(4K₁,net)-free
(4K₁,odd anti-hole,odd-hole)-free
4K₁-free
5-leaf power
5K₁-free
6K₁-free
7K₁-free
(A,T₂,odd-cycle)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AT-free ∩ bipartite
Apollonian network
(C₅,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,K₅ - e,domino ∪ K₁,triangle)-free
(C₅,P₅,gem)-free
(C₅,bull,co-gem,gem)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-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,W_n+4,X₃₁,XF₂ⁿ⁺¹,XF₃ⁿ,C₆,X₃₇,X₉₀,domino,twin-C₅)-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,K₄)-free
(C_n+4,S₃ ∪ K₁,X₁₀₃,claw,eiffeltower,net ∪ K₁)-free
(C_n+4,S₃ ∪ K₁,claw,net)-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
Dilworth 2
(E,odd-cycle)-free
E-free ∩ bipartite
(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
Halin
Helly circle
Helly circular arc
Helly circular arc ∩ (C₇,odd-hole)-free
Helly circular arc ∩ concave-round
Helly circular arc ∩ perfect
Helly circular arc ∩ quasi-line
Helly circular arc ∩ self-clique
(K₂ ∪ claw,triangle)-free
(K_2,3,K₄)-minor-free
(K₃ ∪ 3K₁,C_n+4,co-dart,co-gem)-free
(K_3,3,3,C_n+4)-free
(K_3,3,K_3,3+e,2P₃,C_n+4)-free
(K_3,3,C_n+4)-free
K₄-minor-free
(K₅,X₁₂₆,X₁₇₄,3K₂)-minor-free
N^*
(P,P₅,3K₂,gem)-free
(P,P₅,co-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
(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,gem)-free
(P₆,triangle)-free
PI
PI^*
(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
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
(X₁₀₃,C_n+4,S₃ ∪ K₁,net ∪ K₁,co-claw,co-eiffeltower)-free
(X₁₇₂,triangle)-free
(X₁₇₇,odd-cycle)-free
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free ∩ normal circular arc ∩ quasi-line
β-perfect ∩ co-β-perfect
(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,H)-free
(C_n+4,T₂,X₃₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,T₂,co-XF₂ⁿ⁺¹)-free
(C_n+4,X₅₉,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,odd anti-cycle)-free
(P₇,star_1,2,3,sunlet₄,odd anti-cycle)-free
(P₇,star_1,2,3,odd anti-cycle)-free
(P₇,odd anti-cycle)-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even anti-hole,odd anti-cycle)-free
(T₂,co-cycle)-free
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-free
W_2n+3-free
(X₁₇₇,odd anti-cycle)-free
(X₃₇,co-diamond,even anti-cycle)-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
XC₁₁-free
(XC₁₂,co-cycle)-free
XC₁₂-free
XC₁₃-free
(claw ∪ 3K₁,odd anti-cycle)-free
(star_1,2,3,sunlet₄,odd anti-cycle)-free
(star_1,2,3,odd anti-cycle)-free
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
biconvex
bipartite ∩ bounded tolerance
bipartite ∩ co-comparability
bipartite ∩ convex-round
bipartite ∩ trapezoid
bipartite permutation
bipartite tolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
(bull,co-fork,co-gem)-free
(bull,co-gem,gem)-free
cactus
chordal ∩ circular arc ∩ claw-free
chordal ∩ co-chordal
chordal ∩ hamiltonian ∩ planar
chordal ∩ maximal planar
chordal ∩ planar
chordal ∩ proper circular arc
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 ∪ 3K₁,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 ∩ comparability
co-comparability ∩ tolerance
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 2
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-planar
co-probe cograph
co-proper interval bigraph
co-strongly chordal
comparability ∩ split
comparability graphs of dimension 2 posets
comparability graphs of semiorders
concave-round
containment graph of intervals
even anti-cycle-free
hamiltonian ∩ split
intersection graphs of parallelograms (squares)
k-outerplanar
k-path graph, fixed k
k-polygon
k-tree, fixed k
leaf power ∩ min leaf power
maximal outerplanar
min leaf power
mock threshold ∩ split
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd-cycle,star_1,2,3,sunlet₄)-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
permutation
probe P₄-reducible
probe P₄-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 interval bigraph
proper tolerance
pseudo-split
series-parallel
split
split ∩ strongly chordal
split ∩ superperfect
strong tree-cograph
threshold signed
threshold tolerance
trapezoid
tree-cograph
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
unicyclic
unit Helly circle
unit Helly circular arc
unit circular arc
unit interval bigraph
unit tolerance

GI-complete

NP-hard

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
(2K₃ + e,X₉₈,house)-free
(2K₃ + e,X₉₉,house)-free
(2K₃ + e,house)-free
(2K₃,2K₃ + e,A,H,X₄₅,XZ₅,co-domino)-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
3-DIR
3-DIR contact
3-circular track
3-interval
3-mino
3-track
4-colorable
(4-fan,K_1,4,W₄,W₅,A ∪ K₁,co-fork ∪ K₁,gem ∪ K₁,net ∪ K₁)-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,T₂,X₁₇₂)-free
(5-pan,T₂,X₁₇₂)-free ∩ planar
5-regular
5-regular ∩ hamiltonian
6-colorable
(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
B₀-VPG
B₀-VPG ∩ bipartite
B₀-VPG ∩ triangle-free
B₁-CPG
B₁-CPG ∩ triangle-free
B₁-VCPG
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,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,K₄,diamond)-free ∩ planar
(C₄,C₅)-free
(C₄,S₃)-free
(C₄,A,H)-free
(C₄,co-claw)-free
(C₄,diamond)-free
(C₄,triangle)-free
(C₄,triangle)-free ∩ planar
C₄-free
(C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄,triangle)-free
(C₅,P,P,bull,co-fork,gem,house)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free
(C₅,S₃,3K₂,P₂ ∪ P₄)-free
(C₅,house)-free
C₅-free
(C₆,C₆)-free
(C₆,house)-free
(C₆,triangle)-free
C₆-free
(C₇,odd anti-hole)-free
CONV
CPG
(E,P)-free
E-free
E-free ∩ planar
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
(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,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,K₅)-minor-free
(K₄,S₃,X₃₆,C₇,X₁₇₅,X₁₇₆,X₄₂,antenna,co-claw,net,odd-hole)-free
(K₄,S₃)-free
(K₄,odd anti-hole,odd-hole)-free
K₄-free
K₄-free ∩ map
K₄-free ∩ perfect
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
K₅-free
K₆-free
K₇-free
Meyniel
(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
P₄-bipartite
P₄-brittle
P₄-comparability
PURE-2-DIR
PURE-3-DIR
PURE-k-DIR
(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
(S₃,3K₂,E,odd-hole)-free ∩ line
(S₃,C_n+6,X₃₇,antenna,co-claw,co-sun)-free
(S₃,co-claw,net)-free
(S₃,co-claw)-free
(S₃,net)-free
(S₃,net)-free ∩ sun-free
S₃-free
SEG
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,claw,gem,odd-hole)-free
(W₄,claw,gem)-free
(W₄,claw)-free
(W₄,gem)-free
(W₄,gem)-free ∩ short-chorded
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
XC₁₀-free
(XC₁₁,claw,diamond)-free
(XC₁₁,odd-cycle)-free
(XC₁₁,odd-cycle)-free ∩ planar
XC₁₃-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 C(G)-perfect
cal P₃-perfect
2P₃-free
(3K₂,odd-hole,paw)-free
(5-pan,T₂,X₁₇₂)-free
(A,P₆,co-domino)-free
BW₃-free
C₆-free
(C₇,odd-hole)-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
(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
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
linear domino ∩ maximum degree 4
locally bipartite
locally chordal
locally perfect
locally split
map
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 ∪ K₁-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
universally signable
upper domination perfect
upper irredundance perfect
very strongly perfect
weak bar visibility
weak bisplit
weak rectangle visibility
weakly geodetic

coNP-complete

Open

Unknown to ISGCI

(0,2)-graph
(0,2)-graph ∩ bipartite
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-bounded tripartite
(2,2)-colorable ∩ chordal
2-connected ∩ (4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
2-connected ∩ (P₆,claw)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-strongly regular
2-strongly regular ∩ planar
2-thin
2-threshold
(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,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,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,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,2P₃,C₅,C₆,C₇,K_2,3,K₃ ∪ P₃,W₄,X₈₄,X₉₅,A,C₆,P₆,X₅,X₉₈,butterfly,co-domino,co-fish,fish)-free
(2K₃,2P₃,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
(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,triangle)-free
2P₃-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-Helly
(3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,K₅ - e,co-claw,net,odd anti-hole,twin-house)-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
(3K₂,triangle)-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
3d grid
(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
(5,2)-chordal
(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-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
(6,1)-chordal
(6,1)-chordal ∩ bipartite
(6,1)-even-chordal
(6,2)-chordal
(6,3)
(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
(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,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,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
(A,P₆,domino)-free
AT-free
AT-free ∩ claw-free
B₀-CPG
B₀-VPG ∩ chordal
B₀-VPG ∩ strongly chordal
(BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-free
BW₃-free ∩ modular
Birkhoff
(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,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,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,T₂)-free
(C₄,C₅)-free ∩ Helly
(C₄,C₅)-free ∩ cop-win
(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,K₄,claw,diamond)-free
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,X₉₁,claw)-free
(C₄,claw,diamond)-free
(C₄,odd-hole)-free
C₄-free ∩ C₆-free ∩ bipartite
C₄-free ∩ induced-hereditary pseudo-modular
C₄-free ∩ odd-signable
C₄-free ∩ perfect
(C₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,gem,house)-free
(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,K_3,3-e,T₂,X₁₈,X₉₄,domino,triangle)-free
(C₅,P,P₅,P,bull,co-gem,fork)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,house)-free
(C₅,P,co-fork,fork,gem,house)-free
(C₅,P₂ ∪ P₃,house)-free
(C₅,P₅,A,C₆,P₆,co-domino)-free
(C₅,P₅,C₆,C₇,C₈,P₈,X₁₉,X₂₀,X₂₁,X₂₂,co-gem)-free
(C₅,P₅,P,co-fork,co-gem,fork)-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 ∩ co-line
(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,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,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,S₃,C_n+4 ∪ K₁,W₄,W₅,co-claw,net)-free
(C₆,C₆)-free murky
C₆-free ∩ modular
CIS
(C_n+3 ∪ K₁,diamond,paw)-free
(C_n+4,H)-free
(C_n+4,S₃,net)-free
(C_n+4,S₃)-free
(C_n+4,T₂,XF₂ⁿ⁺¹)-free
(C_n+4,T₂,net)-free
(C_n+4,X₅₉,longhorn)-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+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,odd-cycle)-free
C_n+6-free
C_n+7-free
D
Delaunay
Deza
Dilworth 3
Dilworth 4
(E,triangle)-free
EPT ∩ chordal
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 chordal
Helly chordal ∩ clique-chordal
Helly subtree
Hilbertian
H_n,q grid
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K_1,4,odd-cycle)-free
(K_1,4,odd-cycle)-free ∩ planar
(K_1,4,paw)-free
K_1,4-free ∩ almost claw-free ∩ locally connected
K_1,4-free ∩ well covered
(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,P,P₅)-free
(K_2,3,P,hole)-free
(K_2,3,P₅)-free
(K_2,3,diamond)-free ∩ weakly modular
K_2,3-free ∩ hereditary modular
(K_3,3 ∪ K₁,K₄,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,C₇,X₃₈,X₃₉,butterfly ∪ K₁,co-diamond)-free
(K_3,3,P₅)-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,P₅,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉)-free
(K₄,P₅)-free
(K₄,claw,diamond)-free
(K₄,co-gem)-free
(K₄,odd anti-hole,odd-hole)-free ∩ dually chordal
K₄-free ∩ dually chordal ∩ perfect
Laman
Laman ∩ planar
Matula perfect
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
Mycielski
N^*-perfect
(P,P₅)-free
(P,P₇)-free
(P,P₈)-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,triangle)-free
P₂ ∪ P₄-free
P₄-indifference
P₄-laden
P₄-simplicial
(P₅,S₃,A,E,X₁,anti-hole,co-domino,co-rising sun,net)-free
(P₅,X₈₂,X₈₃)-free
(P₅,A,P₆,anti clique wheel,anti-hole,co-domino)-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,co-sun)-free
(P₅,anti-hole,co-domino)-free
(P₅,anti-hole,co-gem)-free
(P₅,anti-hole)-free
(P₅,bull,odd anti-hole)-free
(P₅,bull)-free
(P₅,claw)-free
(P₅,co-domino,co-gem)-free
(P₅,co-fork)-free
(P₅,cricket)-free
(P₅,fork)-free
(P₅,house)-free
P₅-free
P₅-free ∩ tripartite
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
P₆-free ∩ tripartite
(P₇,odd-cycle)-free
P₇-free
P₇-free ∩ bipartite
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,claw,net)-free
(S₃,net)-free ∩ chordal
S₃-free ∩ chordal
Urquhart
V-perfect
Welsh-Powell opposition
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal
X-conformal
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X₃₇,diamond,even-cycle)-free
(X₇₉,X₈₀)-free ∩ modular
(X₉₁,claw)-free
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
XC₁₀-free ∩ pseudo-modular
XC₁₀-free ∩ weakly modular
(XC₁₂,triangle)-free
(XC₁₂,triangle)-free ∩ planar
(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
β-perfect
β-perfect ∩ perfect
(C_n+3 ∪ K₁,co-diamond,co-paw)-free
(K_1,4,co-diamond)-free
(K_1,4,co-paw)-free
(P,fork)-free
(W₄,W₅,co-butterfly)-free
(W₄,co-claw,co-gem,odd anti-hole)-free
(W₄,co-claw,co-gem)-free
(W₄,co-claw)-free
(W₄,co-gem)-free
W_n+4-free
XC₁₀-free
τ_k-perfect for all k >= 2
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
b-perfect ∩ chordal
balanced ∩ chordal
balanced ∩ co-line
bar visibility
basic 4-leaf power
biclique separable
bigeodetic
binary Hamming
bipartable
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
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 ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ unit grid intersection
bipartite ∩ weakly chordal
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
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ domination perfect
chordal ∩ dually chordal
chordal ∩ hamiltonian
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
chordal bipartite
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-P₄-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-comparability
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension d
(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-paw,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-threshold tolerance
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 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
convex-round
cop-win
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cubical
d-trapezoid
diametral path
(diamond,even-cycle)-free
directed path
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
domination
double split
doubled
doubly chordal
dually chordal
dually chordal ∩ tripartite
edge regular
equimatchable
even-cycle-free
even-hole-free
even-hole-free ∩ probe chordal
extended P₄-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
grid graph ∩ maximum degree 3
half-disk Helly
harmonious
hereditary Helly
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 disk-Helly
hereditary dismantlable
hereditary dominating pair
hereditary dually chordal
hereditary homogeneously orderable
hereditary median
hereditary modular
hereditary perfect elimination bipartite
hereditary sat
hereditary weakly modular
(hole,odd anti-hole)-free
(hole,odd-cycle)-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 bigraph
interval containment bigraph
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
leaf power
leaf power ∪ min leaf power
line ∩ mock threshold
line ∩ well covered
line perfect
linear arboricity <= 2
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
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
median
median ∩ planar
middle
mock threshold
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
nK₂-free, fixed n
nP₃-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
path orderable
perfect connected-dominant
planar ∩ strongly regular
planar of maximum degree 3
polyhedral
power-chordal
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
proper 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
rigid circuit
rooted directed path
self-clique
self-complementary
semi-median
semi-square intersection
semiperfectly orderable
slightly triangulated
solid grid graph
solid triangular grid graph
spider graph
split-perfect
square of tree
starlike
strict 2-threshold
strict B₁-VCPG
strong asteroid free
strongly chordal
strongly odd-signable
strongly orderable
strongly regular
substar
subtree filament
subtree overlap
sun-free ∩ weakly chordal
superbrittle
tolerance
tolerance ∩ triangle-free
trapezoepiped
tree-perfect
triangular grid graph
triangulated
unbreakable
undirected path
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
well-partitioned chordal
wing-triangulated