Recognition problem

(0,3)-colorable ∩ chordal
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-bounded bipartite
1-bounded tripartite
(2,0)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
2-bounded bipartite
2-outerplanar
2-split
2-split ∩ perfect
2-subdivision
2-subdivision ∩ planar
2-threshold
2-tree ∩ probe interval
(2C₄,3K₂,C₆,E,P₂ ∪ P₄,P₆,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,odd-cycle)-free
(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,H,S₃,X₁₆₀,X₁₅₉,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,co-claw,co-diamond)-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,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-free
(2K₃ + e,3K₁,C₅,T₂,X₁₈,X₉₄,co-domino)-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,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 + e,X₉₈,house)-free
(2K₃ + e,X₉₉,house)-free
(2K₃ + e,house)-free
(2K₃,2K₃ + e,3K₁,A,H,T₂,X₁₈,X₄₅,co-domino)-free
(2K₃,2K₃ + e,A,H,X₄₅,XZ₅,co-domino)-free
(2K₃,2P₃,C₄,K₃ ∪ P₃,P₄)-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
(2K₃,4K₁,C₇,X₃₈,X₃₉,W₄ ∪ K₁,W₅,X₈₆,X₈₇,X₈₈,X₈₉,X₉₀,butterfly ∪ K₁,diamond)-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
(2P₃,3K₂,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
(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
3-mino
(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,C₅,butterfly,diamond)-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,P₆)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,X₁₇₂)-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,C₅,C₇,P₂ ∪ P₄,X₁₇₃,X₁₁,net)-free
(3K₂,C₅,P₂ ∪ P₄,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,net)-free
(3K₂,C₅,P₂ ∪ P₄,net)-free
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,odd-cycle,sunlet₄)-free
(3K₂,E,P₂ ∪ P₄,net)-free
(3K₂,P,co-gem,house)-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
(4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
(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,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,house)-free
(4K₁,K₄)-free
(4K₁,P₄)-free
(4K₁,C_n+4)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,house)-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-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 ∩ bipartite
(6,2)
(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
(7,3)
(7,5)
(8,4)
(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,P₆,domino,house)-free
(A,H,K_3,3,K_3,3-e,T₂,X₁₈,X₄₅,domino,triangle)-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,clique wheel,domino,hole,house)-free
(A,P₆,domino)-free
(A,T₂,odd-cycle)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AT-free
AT-free ∩ claw-free
(BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-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 ∪ 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
(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,P₄,dart)-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,triangle)-free
(C₄,triangle)-free ∩ planar
C₄-free
C₄-free ∩ C₆-free ∩ bipartite
C₄-free ∩ induced-hereditary pseudo-modular
(C₅,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,K₅ - e,domino ∪ K₁,triangle)-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,C₆,P₆,triangle)-free
(C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄,triangle)-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,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,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,P₆,P₆)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free ∩ co-line
(C₅,S₃,3K₂,P₂ ∪ P₄)-free
(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-butterfly,co-diamond,triangle)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-free
(C₅,house)-free
C₅-free
C₅-free ∩ P₄-extendible
C₅-free ∩ P₄-tidy
(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,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
(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,H)-free
(C_n+4,K₄)-free
(C_n+4,P₅,bull)-free
(C_n+4,S₃ ∪ K₁,X₁₀₃,claw,eiffeltower,net ∪ K₁)-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,claw,net)-free
(C_n+4,claw)-free
(C_n+4,sun)-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,X₃₇,claw,co-antenna,net,sun)-free
(C_n+6,odd-cycle)-free
D
Delaunay
Dilworth 3
Dilworth 4
(E,P)-free
(E,odd-cycle)-free
(E,triangle)-free
E-free
E-free ∩ bipartite
Gallai
(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
(H,triangle)-free
HH-free
HHD-free
HHD-free ∩ co-HHD-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Hamiltonian hereditary
Hamming
Helly
Helly ∩ bridged
Helly ∩ reflexive
Helly chordal
Helly circle
Hilbertian
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K_1,4,diamond)-free
(K_1,4,paw)-free
K_1,4-free
(K_1,5,triangle)-free
(K₂ ∪ K₃,P₄,butterfly)-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,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,P,anti-hole)-free
(K₂ ∪ K₃,P,house)-free
(K₂ ∪ K₃,co-diamond)-free
(K₂ ∪ K₃,house)-free
K₂ ∪ K₃-free
(K₂ ∪ claw,triangle)-free
K₂ ∪ claw-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,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
K_2,3-free ∩ hereditary modular
(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,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,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)-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,odd anti-hole,odd-hole)-free ∩ dually chordal
K₄-free
K₄-free ∩ dually chordal ∩ perfect
K₄-free ∩ perfect
(K₅ - e,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
(K₅,X₁₂₆,X₁₇₄,3K₂)-minor-free
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
N^*
N^*-perfect
(P,P₅,3K₂,gem)-free
(P,P₅,co-fork)-free
(P,P₅)-free
(P,P₇)-free
(P,P₈)-free
(P,T₂)-free
(P,P,co-fork,fork)-free
(P,co-butterfly,co-fork,co-gem)-free
(P,co-fork,co-gem)-free
(P,co-fork)-free
(P,co-gem,house)-free
(P,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,triangle)-free
P₂ ∪ P₄-free
(P₄,2P₃)-free
(P₄,triangle)-free
P₄-brittle
P₄-comparability
P₄-lite
P₄-simplicial
P₄-tidy ∩ perfect
(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,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,bull)-free ∩ interval
(P₅,claw)-free
(P₅,co-domino,co-gem)-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 ∩ weakly chordal
(P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,C₆,P₆,antenna,hole)-free
(P₆,X₃₀,X₈)-free
(P₆,triangle)-free
P₆-free
P₆-free ∩ chordal bipartite
P₆-free ∩ tripartite
(P₇,odd-cycle,star_1,2,3,sunlet₄)-free
(P₇,odd-cycle,star_1,2,3)-free
P₇-free
(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)-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,co-claw,net)-free
(S₃,co-claw)-free
(S₃,net)-free
(S₃,net)-free ∩ chordal
(S₃,net)-free ∩ split
(S₃,net)-free ∩ sun-free
S₃-free
S₃-free ∩ chordal
(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
(T₃,cycle)-free
(W₄,W₅,butterfly)-free
(W₄,claw,gem,odd-hole)-free
(W₄,claw)-free
(W₄,gem)-free
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
(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
(X₁₇₂,triangle)-free
(X₁₇₇,odd-cycle)-free
(X₃₀,XZ₁,XZ₄,longhorn)-free
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₃₇,diamond,even-cycle)-free
(X₃₈,gem,house)-free
(X₇₉,X₈₀)-free
(X₇₉,X₈₀)-free ∩ modular
XC₁₀-free
XC₁₀-free ∩ pseudo-modular
XC₁₀-free ∩ weakly modular
(XC₁₁,claw,diamond)-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,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
(G)-perfect
(2C₄,3K₂,C₆,E,P₂ ∪ P₄,P₆,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,odd anti-cycle)-free
2P₃-free
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,sunlet₄,odd anti-cycle)-free
(A,P₆,co-domino)-free
(A,T₂,odd anti-cycle)-free
BW₃-free
C₆-free
(C_n+4,H)-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-diamond)-free
(C_n+4,co-gem)-free
(C_n+4,co-sun)-free
(C_n+4,net)-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
(E,P)-free
(E,odd anti-cycle)-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,butterfly,fork,gem)-free
(P,co-star_1,2,4)-free
(P,co-star_1,2,5)-free
(P,fork,gem)-free
(P,fork,house)-free
(P,fork)-free
(P,house)-free
P-free
P₂ ∪ P₄-free
P₃-free
(P₆,X₃₀,X₈)-free
P₆-free
(P₇,star_1,2,3,sunlet₄,odd anti-cycle)-free
(P₇,star_1,2,3,odd anti-cycle)-free
P₇-free
(T₂,co-cycle)-free
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-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
(X₁₇₇,odd anti-cycle)-free
(X₃₀,XZ₁,XZ₄,co-longhorn)-free
(X₃₇,co-diamond,even anti-cycle)-free
(X₇₉,X₈₀)-free
(X₈₂,X₈₃,house)-free
XC₁₀-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
XC₁₁-free
(XC₁₂,co-cycle)-free
XC₁₂-free
(claw ∪ 3K₁,odd anti-cycle)-free
(star_1,2,3,sunlet₄,odd anti-cycle)-free
(star_1,2,3,odd anti-cycle)-free
τ_k-perfect for all k >= 2
absolute bipartite retract
absolute reflexive retract
almost-split
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,fork)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
anti-hole-free
b-perfect
b-perfect ∩ chordal
balanced
balanced ∩ co-line
basic perfect
bi-cograph
biclique separable
biclique-Helly
binary Hamming
bipartable
bipartite ∩ bithreshold
bipartite ∩ claw-free
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ quasi-median
bipartite ∩ weakly chordal
bipartite ∪ co-bipartite ∪ co-line graphs of bipartite graphs ∪ line graphs of bipartite graphs
bipolarizable
bisplit
bithreshold
bounded bitolerance
bounded multitolerance
bridged
bridged ∩ clique-Helly
brittle
building-free
building-free ∩ even-signable
building-free ∩ odd-signable
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,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
charming
chordal ∩ circular arc ∩ claw-free
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ diametral path
chordal ∩ dominating pair
chordal ∩ domination perfect
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ sun-free
chordal bipartite
circle
circle ∩ diamond-free
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
(claw ∪ 3K₁,odd-cycle)-free
(claw,co-claw)-free
(claw,diamond)-free
(claw,net)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd-cycle)-free
(claw,paw)-free
claw-free
claw-free ∩ locally connected
claw-free ∩ perfect
claw-free ∩ well covered
clique separable
clique-Helly
clique-Helly ∩ dismantlable
clique-Helly ∩ dismantlable ∩ reflexive
cliquewidth 3
co-2-subdivision
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-bipartite
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bithreshold ∩ split
co-building-free
(co-butterfly,co-gem)-free
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-diamond)-free
(co-claw,co-paw)-free
(co-claw,house)-free
(co-claw,odd anti-cycle)-free
(co-claw,odd anti-hole,odd-hole)-free
co-claw-free
co-comparability
co-comparability ∪ comparability
co-comparability graphs of posets of interval dimension 2
co-comparability graphs of posets of interval dimension 2, height 1
(co-cricket,house)-free
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-domino-free
(co-fork,hole)-free
(co-fork,house)-free
(co-fork,odd anti-cycle)-free
co-fork-free
(co-gem,gem)-free
(co-gem,house)-free
co-gem-free
co-hereditary clique-Helly
co-interval bigraph
co-interval containment bigraph
co-line
co-line graphs of bipartite graphs
(co-odd building,odd anti-hole)-free
(co-paw,odd anti-hole)-free
(co-paw,paw)-free
(co-paw,triangle)-free
co-paw-free
co-planar
co-probe cograph
co-probe threshold
co-proper interval bigraph
co-strongly chordal
co-threshold tolerance
co-trapezoid
cograph contraction
comparability
comparability ∩ split
comparability ∩ weakly chordal
comparability graphs of posets of interval dimension 2
comparability graphs of posets of interval dimension 2, height 1
containment graphs
cop-win
(cross,triangle)-free
cycle-bicolorable
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
disk-Helly
dismantlable
distance regular
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
(domino,gem,house)-free
domino-free
domishold
doubled
dually chordal ∩ tripartite
equimatchable
even anti-cycle-free
even-cycle-free
even-hole-free ∩ probe chordal
(fork,house)-free
(fork,odd-cycle)-free
(fork,triangle)-free
fork-free
gem-free
generalized strongly chordal
genus 1
geodetic
good
half-disk Helly
hereditary Helly
hereditary Matula perfect
hereditary N^*-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary absolute bipartite retract
hereditary biclique-Helly
hereditary clique-Helly
hereditary disk-Helly
hereditary dismantlable
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary median
hereditary modular
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary perfect elimination bipartite
(hole,odd-cycle)-free
hole-free
homogeneously orderable
homogeneously representable
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
interval bigraph
interval containment bigraph
interval regular
interval regular of diameter 2
isometric subgraph of a hypercube
isometric-hereditary pseudo-modular
k-polygon
k-regular, fixed k
kernel solvable
line ∩ perfect
line ∩ well covered
line graphs of Helly hypergraphs of rank 3
line graphs of bipartite multigraphs
line graphs of linear hypergraphs of rank 3
line graphs of triangle-free graphs
linear cliquewidth 2
linear domino
linear domino ∩ maximum degree 4
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
maxibrittle
median
modular
modular ∩ open-neighbourhood-Helly
module-composed
murky
nK₂-free, fixed n
nP₃-free, fixed n
nearly bipartite
neighbourhood-Helly
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
neighbourhood-Helly ∩ triangle-free
net-free
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
(odd-cycle,star_1,2,3,sunlet₄)-free
(odd-cycle,star_1,2,3)-free
odd-hole-free ∩ planar
odd-signable ∩ triangle-free
open-neighbourhood-Helly
overlap
partial 3-tree
partial 3-tree ∩ planar
partial 4-tree
partial cube
paw-free
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect connected-dominant
perfect elimination bipartite
perfectly 1-transversable
planar ∩ triangle-free
premedian
probe P₄-reducible
probe P₄-sparse
probe bipartite chain
probe chordal
probe chordal ∩ weakly chordal
probe interval
probe interval bigraph
probe ptolemaic
probe split
pseudo-median
pseudo-median ∩ triangle-free
pseudo-modular
pseudo-modular ∩ triangle-free
(q,q-4), fixed q
quasi-Meyniel
quasi-brittle
quasi-median
quasitriangulated
semi-median
semicircular
semiperfectly orderable
slightly triangulated
split ∩ strongly chordal
split ∩ superperfect
split-neighbourhood
strictly clique irreducible
strong asteroid free
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly even-signable
strongly odd-signable
strongly orderable
superfragile
threshold tolerance
tolerance ∩ tree
toroidal
totally unimodular
trapezoid
tree-cograph
treewidth 3
treewidth 4
triangle-free
unbreakable
undirected path
very strongly perfect
weakly chordal
weakly geodetic
weakly median
weakly modular
well-dominated
wing-triangulated

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

Problem: Recognition

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI