Cliquewidth expression problem

(0,2)-colorable
(0,3)-colorable
(1,1)-colorable
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-DIR
1-string
(2,0)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
(2,2)-interval
2-DIR
2-interval
2-split
2-split ∩ perfect
2-subdivision
2-subdivision ∩ planar
2-thin
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,X₈₅)-free
(2K₂,3K₁)-free
(2K₂,4K₁,C₅,co-diamond)-free
(2K₂,4K₁,co-claw,co-diamond)-free
(2K₂,A,H)-free
(2K₂,C₄,C₅)-free
(2K₂,C₄)-free
(2K₂,C₅,C₆,C₇,C₈,co-claw,co-diamond)-free
(2K₂,C₅,C₆,net)-free
(2K₂,C₅,T₂)-free
(2K₂,C₅)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,P₆)-free
(2K₂,X₉₁,co-claw)-free
(2K₂,claw)-free
(2K₂,co-diamond)-free
(2K₂,house)-free
(2K₂,net)-free
(2K₂,odd anti-hole)-free
2K₂-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,A,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,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
(2K₃,3K₁,A,H,X₄₅)-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-free
3-DIR
3-DIR contact
3-Helly
3-interval
3-mino
(3K₁,C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄)-free
(3K₁,C₆)-free
(3K₁,H)-free
(3K₁,K_1,5)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,co-cross)-free
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
3d grid
(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,co-claw,co-diamond)-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-crossing-chordal
(5,2)-odd-noncrossing-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
(6,1)-chordal
(6,1)-chordal ∩ bipartite
(6,1)-even-chordal
(6,2)-chordal
(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,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,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 ∩ bipartite
AT-free ∩ chordal
AT-free ∩ claw-free
(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
BW₃-free ∩ modular
Berge
Berge ∩ bull-free
Berge ∩ claw-free
Bouchet
(C₄,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅,triangle)-free
(C₄,C₅,C₆,C₇,C₈,H,X₈₅,triangle)-free
(C₄,C₅,C₆,C₇,C₈,H,X₈₅,triangle)-free ∩ K_1,4-free
(C₄,C₅,C₆,C₇,C₈,claw,diamond)-free
(C₄,C₅,C₆,S₃)-free
(C₄,C₅,K₄,diamond)-free
(C₄,C₅,K₄,diamond)-free ∩ planar
(C₄,C₅,T₂)-free
(C₄,C₅)-free
(C₄,C₅)-free ∩ Helly
(C₄,C₅)-free ∩ cop-win
(C₄,C₆,odd-cycle)-free
(C₄,K₄,claw,diamond)-free
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,S₃)-free
(C₄,X₉₁,claw)-free
(C₄,A,H)-free
(C₄,co-claw)-free
(C₄,diamond)-free
(C₄,odd-hole)-free
(C₄,triangle)-free
(C₄,triangle)-free ∩ planar
C₄-free
C₄-free ∩ C₆-free ∩ bipartite
C₄-free ∩ co-comparability
C₄-free ∩ induced-hereditary pseudo-modular
(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,bull,co-gem,fork)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,house)-free
(C₅,P,P,bull,co-fork,gem,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,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
(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
C₆-free ∩ modular
CONV
(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,S₃ ∪ K₁,X₄₂,T₂,X₂,X₃,odd-cycle ∪ K₁,even anti-hole,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,S₃,claw,net)-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,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,co-XF₁²ⁿ⁺³,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 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
(C_n+6,X₃₇,claw,co-antenna,net,sun)-free
(C_n+6,odd-cycle)-free
C_n+6-free
C_n+7-free
(E,P)-free
E-free
EPT
EPT ∩ chordal
F_n grid
Gallai
Gallai-perfect
(H,triangle)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly
Helly ∩ bridged
Helly chordal
Helly chordal ∩ clique-chordal
Helly circle
Helly circular arc
Hilbertian
H_n,q grid
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K_1,4,diamond)-free
(K_1,4,odd-cycle)-free
(K_1,4,paw)-free
K_1,4-free
(K_1,5,triangle)-free
(K₂ ∪ K₃,P₅,X₃₇,X₃₈,co-diamond,co-domino,co-twin-C₅)-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,co-diamond)-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,diamond)-free ∩ weakly modular
K_2,3-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,K₅)-minor-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,X₃₆,C₇,X₁₇₅,X₁₇₆,X₄₂,antenna,co-claw,net,odd-hole)-free
(K₄,S₃)-free
(K₄,claw,diamond)-free
(K₄,odd anti-hole,odd-hole)-free
K₄-free
K₄-free ∩ perfect
(K₅ - e,W₅,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-C₅,co-twin-house)-free
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N^*
(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,house)-free
P₂ ∪ P₄-free
P₄-bipartite
P₄-brittle
P₄-comparability
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,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 ∩ weakly chordal
(P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,C₆,P₆,antenna,hole)-free
(P₆,X₃₀,X₈)-free
P₆-free
P₇-free
PI
PI^*
PURE-3-DIR
PURE-k-DIR
(S₃,S₄,net)-free
(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
(S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
(S₃,3K₂,E,P₂ ∪ P₄)-free
(S₃,3K₂,E,odd-hole)-free
(S₃,C_n+4 ∪ K₁,C(n,k),W₄,even-hole,odd-cycle ∪ K₁)-free
(S₃,C_n+4 ∪ K₁,W₄,even-hole,net,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,C_n+6,X₃₇,antenna,co-claw,co-sun)-free
(S₃,claw,net)-free
(S₃,claw,net)-free ∩ chordal
(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
(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,hole)-free
(T₂,X₂,X₃,hole,triangle)-free
V-perfect
(W₄,W₅,butterfly)-free
(W₄,claw,gem)-free
(W₄,claw)-free
(W₄,gem)-free
(W₄,gem)-free ∩ short-chorded
Welsh-Powell opposition
Welsh-Powell perfect
X-chordal
X-chordal ∩ X-conformal ∩ bipartite
X-chordal ∩ bipartite
X-conformal
X-conformal ∩ bipartite
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X₁₀₃,C_n+4,S₃ ∪ K₁,net ∪ K₁,co-claw,co-eiffeltower)-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
(X₇₉,X₈₀)-free
(X₇₉,X₈₀)-free ∩ modular
XC₁₀-free
XC₁₀-free ∩ pseudo-modular
(XC₁₁,claw,diamond)-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
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,anti-hole,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,hole)-free
β-perfect
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(G)-perfect
₃-perfect
2P₃-free
(3K₂,odd-hole,paw)-free
(A,P₆,co-domino)-free
BW₃-free
C₆-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,co-claw)-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,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,odd anti-cycle)-free
C_n+6-free
C_n+7-free
(E,P)-free
E-free
(K_1,4,P,co-fork,house)-free
(K_1,4,co-diamond)-free
(K_1,4,co-paw)-free
(K_1,4,house)-free
(K_1,4,odd anti-cycle)-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,fork)-free
(P,house)-free
P-free
P₂ ∪ P₄-free
(P₆,X₃₀,X₈)-free
P₆-free
P₇-free
(W₄,W₅,co-butterfly)-free
(W₄,co-claw,co-gem)-free
(W₄,co-claw)-free
(W₄,co-gem)-free
(X₃₀,XZ₁,XZ₄,co-longhorn)-free
(X₇₉,X₈₀)-free
(X₈₂,X₈₃,house)-free
XC₁₀-free
(XC₁₁,co-claw,co-diamond)-free
XC₁₁-free
XC₁₂-free
(n+4)-pan-free
τ_k-perfect for all k >= 2
absolute bipartite retract
absolutely perfect
absorbantly perfect
all-4-simplicial
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,bull,odd-hole)-free
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
(anti-hole,odd-hole)-free
anti-hole-free
astral triple-free
b-perfect
b-perfect ∩ chordal
balanced
balanced 2-interval
balanced ∩ paw-free
biclique separable
biclique-Helly
biconvex
bip^*
bipartite
bipartite ∩ bounded tolerance
bipartite ∩ co-comparability
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ maximum degree 3
bipartite ∩ probe interval
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ weakly chordal
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite permutation
bipartite tolerance
biplanar
bisplit
bisplit ∩ triangle-free
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,odd-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 ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ co-comparability
chordal ∩ diametral path
chordal ∩ dominating pair
chordal ∩ domination perfect
chordal ∩ dually chordal
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ proper circular arc
chordal ∩ sun-free
chordal ∩ unit circular arc
chordal ∪ co-chordal
chordal bipartite
circle
circle ∩ diamond-free
circle graph with equator
circle-polygon
circular arc
circular arc ∩ co-bipartite
circular arc ∩ comparability
circular convex bipartite
circular perfect
circular permutation
(claw,diamond)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd-hole)-free
claw-free
claw-free ∩ interval
claw-free ∩ perfect
claw-free ∩ upper domination perfect
clique
clique separable
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-chordal
clique-perfect
clique-perfect ∩ triangle-free
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-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bounded tolerance
co-building-free
(co-butterfly,co-gem)-free
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-circular perfect
(co-claw,co-diamond)-free
(co-claw,house)-free
(co-claw,odd anti-hole,odd-hole)-free
(co-claw,odd anti-hole)-free
(co-claw,odd-hole)-free
co-claw-free
co-comparability
co-comparability ∩ comparability
co-comparability ∩ 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 1
co-comparability graphs of posets of interval dimension d
(co-cricket,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-domino-free
(co-fork,hole)-free
(co-fork,house)-free
co-fork-free
co-gem-free
co-hereditary clique-Helly
co-interval
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-interval filament
co-interval mixed
co-line
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
co-paw-free
co-perfectly orderable
co-planar
co-proper interval bigraph
co-strongly chordal
co-sun-free
co-threshold tolerance
co-tolerance
co-trapezoid
cograph contraction
coin
comparability
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 1
comparability graphs of posets of interval dimension d
comparability graphs of semiorders
concave-round
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex
convex-round
cop-win
(cross,triangle)-free
cycle-bicolorable
d-trapezoid
diametral path
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
directed path
disk
disk contact
disk-Helly
dismantlable
dominating pair
domination
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
domino
(domino,gem,house)-free
domino-free
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,house)-free
fork-free
gem-free
generalized strongly chordal
genus 0
genus 1
good
graceful
grid
grid intersection
half-disk Helly
hereditary Helly
hereditary Matula perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary X-chordal
hereditary absolute bipartite retract
hereditary biclique-Helly
hereditary clique-Helly
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary disk-Helly
hereditary dismantlable
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary modular
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary perfect elimination bipartite
hereditary weakly modular
(hole,odd anti-hole)-free
(hole,odd-cycle)-free
hole-free
homogeneously orderable
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
indifference
induced-hereditary pseudo-modular
intersection graphs of parallelograms (squares)
interval
interval bigraph
interval containment bigraph
interval enumerable
interval filament
irredundance perfect
irredundance perfect with ir(G)<= 4
isometric-HH-free
isometric-hereditary pseudo-modular
k-DIR
k-polygon
k-starlike
kernel solvable
line
line graphs of Helly hypergraphs of rank 3
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 connected
locally perfect
max-tolerance
maxibrittle
maximal clique irreducible
maximum degree 3
maximum degree 4
median
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
(n+4)-pan-free
nK₂-free, fixed n
nP₃-free, fixed n
nearly bipartite
neighbourhood perfect
neighbourhood-Helly
neighbourhood-Helly ∩ triangle-free
net-free
normal
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-cycle-free
(odd-hole,paw)-free
odd-hole-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable
odd-sun-free
open-neighbourhood-Helly
opposition
outer-string
overlap
(p,q<=2)-colorable
p-connected
parity
partial 3d grid
partial bar visibility
partial grid
partial rectangle visibility
path orderable
paw-free
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect connected-dominant
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
permutation
planar
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polar
power-chordal
preperfect
pretty
probe AT-free
probe Gallai
probe HHDS-free
probe Meyniel
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-comparability
probe comparability
probe interval
probe interval bigraph
probe permutation
probe split
probe strongly chordal
probe unit interval
proper Helly circular arc
proper circular arc
proper interval
proper interval bigraph
proper tolerance
pseudo-median
pseudo-modular
pseudo-modular ∩ triangle-free
pseudo-split
quasi-Meyniel
quasi-brittle
quasi-line
quasi-median
quasi-parity
quasitriangulated
rectangle visibility
semi-square intersection
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
spider graph
split
split-neighbourhood
split-perfect
strict quasi-parity
string
strong asteroid free
strong domination perfect
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly even-signable
strongly orderable
strongly perfect
subtree filament
subtree overlap
sun-free
sun-free ∩ weakly chordal
superbrittle
superperfect
thickness <= 2
threshold tolerance
tolerance
tolerance ∩ triangle-free
toroidal
totally unimodular
trapezoid
triangle contact
triangle-free
triangulated
tripartite
undirected path
unimodular
unit 2-interval
unit Helly circular arc
unit circular arc
unit disk
unit interval
unit interval bigraph
unit tolerance
upper domination perfect
upper irredundance perfect
very strongly perfect
visibility
weak bar visibility
weak bipolarizable
weak bisplit
weak dominating pair
weak rectangle visibility
weakly chordal
weakly geodetic
weakly modular

Input:	A graph G in this class.
Output:	An expression that constructs G according to the rules for cliquewidth, using only a constant number of labels. Undefined if this class has unbounded cliquewidth.

Problem: Cliquewidth expression

Linear

Polynomial

NP-hard

Unbounded or NP-complete

coNP-complete

Open

Unknown to ISGCI