Monopolarity problem

(1,2)-polar
1-bounded tripartite
(2,0)-colorable
2-connected ∩ (P₆,claw)-free
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,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,K_3,3,K_3,3+e,P₄,2P₃)-free
(2K₂,P₄,2P₃)-free
(2K₂,P₄,co-dart)-free
(2K₂,P₄)-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 + 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,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 + 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
(2K₃,2K₃ + e,3K₁,A,H,T₂,X₁₈,X₄₅,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
(2K₃,3K₁,A,H,X₄₅)-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,P₄)-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
(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,P₄)-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,P₃)-free
(3K₁,P₆)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,X₁₇₂)-free
(3K₁,XC₁₂)-free
(3K₁,co-cross)-free
(3K₁,co-fork)-free
(3K₁,house)-free
(3K₁,paw)-free
3K₁-free
(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,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,C₅,P₂ ∪ P₄,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,net)-free
(3K₂,co-paw,odd anti-hole)-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
(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,K₄)-free
(4K₁,P₄)-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
(5,1)
(5,2)-chordal
(5,2)-crossing-chordal
(5-pan,T₂,X₁₇₂)-free
(5-pan,T₂,X₁₇₂)-free ∩ planar
(6,2)
6K₁-free
(7,3)
7K₁-free
(8,4)
(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,P₆,clique wheel,domino,hole,house)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AT-free ∩ claw-free
Berge ∩ claw-free
(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,P₅)-free
(C₄,X₉₁,claw)-free
(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,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,bull,co-gem,fork)-free
(C₅,P,P₅,P,co-fork,fork,house)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,house)-free
(C₅,P,co-fork,fork,gem,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,gem)-free
(C₅,P₅,house)-free
(C₅,P₅)-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-free ∩ P₄-extendible
C₅-free ∩ P₄-tidy
C₅-free ∩ matrogenic
(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,P₆,P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,anti-hole,co-antenna)-free
(C₆,C₆)-free murky
(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 ∪ 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+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,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
Dilworth 2
Dilworth 3
(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
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDA-free
HHDG-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Helly circular arc ∩ concave-round
Helly circular arc ∩ quasi-line
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K₂ ∪ K₃,P₄,butterfly)-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,P,X₁₆₃,X₉₅,co-diamond,house)-free
(K₂ ∪ K₃,co-diamond)-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
(K_2,3,P,P₅)-free
(K_2,3,P,hole)-free
(K_2,3,P₄,co-butterfly)-free
(K_2,3,P₅)-free
(K₃ ∪ 3K₁,C_n+4,co-dart,co-gem)-free
(K_3,3 ∪ K₁,K₄,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,C₇,X₃₈,X₃₉,butterfly ∪ K₁,co-diamond)-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,P₄)-free
(K₄,P₅,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉)-free
(K₄,P₅)-free
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N^*
(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,P₅)-free
(P,P,co-fork,fork)-free
(P₃ ∪ 2K₁,C_n+4,X₁₀₂,X₂₀₄,co-gem)-free
(P₄,2P₃)-free
(P₄,co-cycle)-free
P₄-extendible
P₄-extendible ∩ P₄-sparse
P₄-free
P₄-indifference
P₄-laden
P₄-lite
P₄-reducible
P₄-simplicial
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,A,E,X₁,anti-hole,co-domino,co-rising sun,net)-free
(P₅,S₃,anti-hole,co-domino,co-gem)-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,P,gem)-free
(P₅,P₂ ∪ P₃)-free
(P₅,X₃₈,co-gem)-free
(P₅,anti-hole,co-bicycle,co-domino)-free
(P₅,anti-hole,co-domino,co-gem)-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,co-fork)-free
(P₅,bull,house)-free
(P₅,bull,odd anti-hole)-free
(P₅,bull)-free
(P₅,claw)-free
(P₅,co-domino,co-gem)-free
(P₅,co-fork,house)-free
(P₅,co-fork)-free
(P₅,cricket)-free
(P₅,diamond)-free
(P₅,fork,house)-free
(P₅,fork)-free
(P₅,gem)-free
(P₅,house)-free
(P₅,triangle)-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,claw)-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,claw,net)-free
(S₃,net)-free ∩ extended P₄-sparse
(W₄,claw,gem,odd-hole)-free
(W₄,claw,gem)-free
(W₄,claw)-free
Welsh-Powell opposition
(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
(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
(X₉₁,claw)-free
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
(XC₇,XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₈)-free
XC₉-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
(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+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,X₅₉,co-longhorn)-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-claw)-free
(C_n+4,co-dart,co-gem)-free
(C_n+4,co-diamond)-free
(C_n+4,co-gem)-free
(C_n+4,co-sun)-free
(C_n+4,net)-free
(C_n+4,odd co-sun)-free
C_n+4-free
(C_n+6,odd anti-cycle)-free
(E,odd anti-cycle)-free
(K_1,4,co-diamond)-free
(K_1,4,co-paw)-free
(K_1,4,odd anti-cycle)-free
(P,butterfly,fork,gem)-free
(P,fork,gem)-free
(P,fork,house)-free
(P,fork)-free
P₃-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
odd-cycle ∪ K₁-free
(star_1,2,3,sunlet₄,odd anti-cycle)-free
(star_1,2,3,odd anti-cycle)-free
absolutely perfect
almost-split
alternately orientable ∩ co-comparability
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,co-sun,hole)-free
(anti-hole,fork)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
b-perfect
biclique separable
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipartite ∪ co-bipartite ∪ split
bipolarizable
bithreshold
bitolerance
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
brittle
(bull,co-fork,fork)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,fork)-free
(bull,hole,odd anti-hole)-free
(butterfly,claw)-free
charming
chordal ∪ co-chordal
chordal-perfect
circle graph with equator
circular arc ∩ co-bipartite
circular arc ∩ cograph
circular interval
(claw,co-claw)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free
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 ∩ perfect
claw-free ∩ upper domination perfect
claw-free ∩ well covered
clique graphs of Helly circular arc
clique graphs of normal Helly circular arc
cliquewidth 2
co-2-subdivision
co-Gallai
co-HHD-free
co-Meyniel
co-Welsh-Powell opposition
co-β-perfect
co-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bounded tolerance
co-building-free
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
co-cluster
co-comparability
co-comparability ∩ comparability
co-comparability ∩ tolerance
co-comparability graphs of dimension d posets
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 2
co-comparability graphs of posets of interval dimension d
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,even anti-cycle)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-forest-perfect
(co-fork,hole)-free
(co-fork,odd anti-cycle)-free
co-interval
co-interval ∩ cograph
co-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-leaf power
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
(co-paw,paw)-free
(co-paw,triangle)-free
co-paw-free
co-planar
co-probe cograph
co-proper interval bigraph
co-strongly chordal
co-tolerance
co-trapezoid
co-trivially perfect
cograph
cograph contraction
comparability ∩ distance-hereditary
comparability ∩ weakly chordal
comparability graphs of dimension 2 posets
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension 2, height 3
comparability graphs of semiorders
comparability graphs of series-parallel posets
complete multipartite
concave-round
containment graph of intervals
d-trapezoid
distance-hereditary
domination
domino
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
domishold
even anti-cycle-free
even-hole-free ∩ probe chordal
extended P₄-laden
extended P₄-reducible
extended P₄-sparse
forest-perfect
(fork,house)-free
(fork,triangle)-free
fork-free
fuzzy circular interval
fuzzy linear interval
generalized strongly chordal
good
hereditary Matula perfect
hereditary N^*-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary homogeneously orderable
hereditary sat
(hole,odd anti-hole)-free
hole-free
hole-free ∩ planar
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
intersection graphs of parallelograms (squares)
leaf power ∪ min leaf power
line graphs of bipartite multigraphs
line graphs of multigraphs without triangles
linear cliquewidth 2
matrogenic
matroidal
maxibrittle
maximal planar
middle
min leaf power
mock threshold
module-composed
multitolerance
odd anti-cycle-free
parallelepiped
perfect connected-dominant
permutation
probe HHDS-free
probe P₄-reducible
probe bipartite distance-hereditary
probe chordal ∩ weakly chordal
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe proper interval
probe ptolemaic
probe strongly chordal
probe threshold
probe trivially perfect
probe unit interval
proper Helly circular arc
proper circular arc
proper tolerance
quasi-brittle
quasi-line
quasitriangulated
semi-P₄-sparse
semicircular
semiperfectly orderable
split-perfect
strict 2-threshold
strong tree-cograph
strongly orderable
sun-free ∩ weakly chordal
superbrittle
threshold signed
threshold tolerance
tolerance
trapezoepiped
trapezoid
tree-cograph
tree-perfect
unit Helly circular arc
unit circular arc
unit tolerance
weak bipolarizable
weakly chordal

Input:	A graph G in this class.
Output:	True iff G is monopolar.

Problem: Monopolarity

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI