Information System on Graph Classes and their Inclusions

Problem: Independent dominating set

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI

• (0,2)-graph
• (0,2)-graph ∩ bipartite
• 1-bounded tripartite
• (2,1)-colorable
• 2-connected
• 2-connected ∩ (P₆,claw)-free
• 2-connected ∩ cubic ∩ planar
• 2-connected ∩ linearly convex triangular grid graph
• 2-edge-connected
• 2-strongly regular
• 2-strongly regular ∩ planar
• 2-subdivision
• 2-subdivision ∩ planar
• 2-thin
• 2-threshold
• (2K₂,A,C₅,S₃,X₁₅₉,X₂₁₉,C₆,E,P₆,X₁₅₉,X₂₁₉,X₅₈,co-rising sun,net,rising sun)-free
• (2K₂,A,C₅,2P₃,X₁₇₀,house)-free
• (2K₂,A,H)-free
• (2K₂,C₄)-free
• (2K₂,C₅,C₆,C₇,C₈)-free
• (2K₂,C₅,C₆,net)-free
• (2K₂,C₅,T₂)-free
• (2K₂,C₅)-free
• (2K₂,2P₃,C₆)-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
• (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
• (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,C₆)-free
• (2P₃,triangle)-free
• (2P₄,A,C₅,C₆,C₇,E,K_3,3-e,P₇,R,X₁,X₁₀₃,X₅,X₅₈,X₈₄,X₉₈,C₆,P₆,X₅,sunlet₄,co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free
• 3-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,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,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
• (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-regular
• 4-regular ∩ hamiltonian
• 4-regular ∩ hamiltonian ∩ planar
• 4-regular ∩ planar
• (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-pan,T₂,X₁₇₂)-free ∩ planar
• 5-regular
• 5-regular ∩ hamiltonian
• 5-regular ∩ hamiltonian ∩ planar
• 5-regular ∩ planar
• (6,1)-chordal ∩ bipartite
• (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,E,P₆,S₃,X₁₅₉,X₂₁₉,X₅,X₅₈,A,C₆,E,P₆,X₁₅₉,X₂₁₉,X₅,X₅₈,antenna,co-antenna,co-domino,co-rising sun,domino,net,rising sun)-free
• (A,C₅,C₆,E,P₆,S₃,X₁₅₉,X₂₁₉,X₅₈,A,X₁₅₉,X₂₁₉,co-rising sun,domino,house,net,rising sun)-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,S₃,X₁₅₉,X₂₁₉,A,C₆,E,P₆,X₁₅₉,X₂₁₉,X₅₈,co-domino,co-rising sun,net,rising sun)-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
• (A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
• AT-free
• AT-free ∩ bipartite
• AT-free ∩ claw-free
• B₀-CPG
• (BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-free
• BW₃-free ∩ modular
• Berge ∩ claw-free
• 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,XC₁₁,claw,diamond)-free
• (C₄,C₅,T₂)-free
• (C₄,C₅)-free ∩ Helly
• (C₄,C₅)-free ∩ cop-win
• (C₄,K₄,claw,diamond)-free
• (C₄,P₅)-free
• (C₄,P₆)-free
• (C₄,X₉₁,claw)-free
• (C₄,claw,diamond)-free
• C₄-free ∩ odd-signable
• C₄-free ∩ weakly modular
• (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 ∪ 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+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,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
• D
• Delaunay
• Deza
• Dilworth 2
• Dilworth 3
• Dilworth 4
• (E,triangle)-free
• E-free ∩ planar
• F_n grid
• Gabriel
• (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
• 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 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
• Helly subtree
• Hilbertian
• H_n,q grid
• (K_1,4,P,P₅,fork)-free
• (K_1,4,P₅)-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_3,3,3,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,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
• (K₅ - e,S₃,3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
• (K₅ - e,A,C₄ ∪ 2K₁,P₂ ∪ P₃,R,claw,co-twin-house,odd-hole)-free
• Laman
• Laman ∩ planar
• Matula perfect
• Meyniel ∩ co-Meyniel
• Meyniel ∩ weakly chordal
• Mycielski
• N^*
• 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,P,anti-hole)-free
• (P₅,P₂ ∪ P₃)-free
• (P₅,P₆,anti-hole)-free
• (P₅,P₆)-free
• (P₅,P₆)-free ∩ weakly chordal
• (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,hole,house)-free
• (P₆,house)-free
• P₆-free
• P₆-free ∩ tripartite
• (P₇,odd-cycle)-free
• P₇-free ∩ bipartite
• PI
• PI^*
• 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,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,X₄₂)-free
• (S₃,3K₂,E,odd-hole)-free ∩ line
• (S₃,C_n+4 ∪ K₁,C(n,k),W₄,even-hole,odd-cycle ∪ K₁)-free
• (S₃,C_n+4,S₃ ∪ K₁,co-claw)-free
• (S₃,C_n+4,T₂)-free
• (S₃,C_n+4,co-claw,net)-free
• (S₃,C_n+4,co-claw)-free
• (S₃,C_n+4,net)-free
• (S₃,claw,net)-free
• (T₂,X₂,X₃,hole,triangle)-free
• (T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even-hole,odd-cycle)-free
• Urquhart
• V-perfect
• (W₄,claw,gem,odd-hole)-free
• (W₄,claw,gem)-free
• (W₄,claw)-free
• Welsh-Powell opposition
• Welsh-Powell perfect
• X-chordal
• X-chordal ∩ X-conformal
• X-conformal
• X-conformal ∩ bipartite ∩ hereditary X-chordal
• X-star-chordal
• (X₁₀₃,C_n+4,S₃ ∪ K₁,net ∪ K₁,co-claw,co-eiffeltower)-free
• (X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
• (X₃₇,diamond,even-cycle)-free
• (X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free ∩ normal circular arc ∩ quasi-line
• (X₇₉,X₈₀)-free ∩ modular
• (X₉₁,claw)-free
• (XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-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,hole)-free
• β-perfect
• β-perfect ∩ co-β-perfect
• (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,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
• (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
• (X₃₇,co-diamond,even anti-cycle)-free
• XC₁₀-free
• absolute bipartite retract
• absolute reflexive retract
• absolutely perfect
• almost median
• almost-split
• alternately colourable
• alternately orientable ∩ co-comparability
• (anti-hole,co-sun,hole)-free
• (anti-hole,fork)-free
• (anti-hole,hole,sun)-free
• b-perfect
• balanced ∩ co-line
• balanced ∩ line
• bar visibility
• biconvex
• bigeodetic
• binary Hamming
• bipartable
• bipartite ∩ bounded tolerance
• bipartite ∩ co-comparability
• bipartite ∩ co-perfectly orderable
• bipartite ∩ co-trapezoid
• bipartite ∩ convex-round
• bipartite ∩ cubic ∩ planar
• bipartite ∩ mock threshold
• bipartite ∩ probe interval
• bipartite ∩ quasi-median
• bipartite ∩ tolerance
• bipartite ∩ trapezoid
• bipartite ∩ unit grid intersection
• bipartite ∩ weakly chordal
• bipartite permutation
• bipartite tolerance
• bipolarizable
• bithreshold
• bitolerance
• bounded bitolerance
• bounded cutwidth
• bounded degree
• bounded degree ∩ bounded treewidth
• bounded multitolerance
• bounded tolerance
• 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 ∪ co-chordal
• chordal bipartite
• chordal-perfect
• circle
• circle ∩ diamond-free
• circle graph with equator
• circle-n-gon, fixed n
• circle-polygon
• circle-trapezoid
• circular arc
• circular arc ∩ clique-Helly
• circular arc ∩ comparability
• circular arc ∩ diamond-free
• circular arc ∩ paw-free
• circular arc ∩ perfect
• circular convex bipartite
• circular interval
• circular permutation
• circular strip
• circular trapezoid
• (claw,diamond,odd-hole)-free
• (claw,diamond)-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-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
• 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-β-perfect
• co-bithreshold
• co-bounded tolerance
• co-building-free
• (co-butterfly,co-gem)-free
• co-chordal
• co-chordal ∩ comparability
• co-chordal ∩ superperfect
• (co-claw,co-diamond,odd anti-hole)-free
• (co-claw,co-diamond)-free
• 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 d
• (co-diamond,even anti-cycle)-free
• (co-diamond,odd anti-hole)-free
• co-diamond-free
• co-forest-perfect
• (co-fork,hole)-free
• co-gem-free
• co-hereditary clique-Helly
• co-interval
• co-interval ∪ interval
• co-leaf power
• 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-strongly chordal
• co-tolerance
• co-trapezoid
• co-unit interval
• cograph contraction
• 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 2
• comparability graphs of posets of interval dimension 2, height 3
• comparability graphs of posets of interval dimension d
• comparability graphs of semiorders
• complete Hamming
• concave-round
• containment graph of circles
• containment graph of intervals
• containment graphs of circular arcs
• convex
• convex-round
• cop-win
• cubic
• cubic ∩ hamiltonian
• cubic ∩ hamiltonian ∩ planar
• cubic ∩ planar
• cubical
• d-trapezoid
• diametral path
• (diamond,even-cycle)-free
• disk-Helly
• dismantlable
• distance regular
• distance regular of diameter 2
• domination
• domination perfect ∩ planar
• domino
• double split
• doubled
• dually chordal
• dually chordal ∩ tripartite
• edge regular
• equimatchable
• even anti-cycle-free
• even-cycle-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
• galled-tree explainable
• galled-tree explainable ∩ house-free
• generalized strongly chordal
• generically minimally rigid
• geodetic
• good
• graceful
• grid
• grid graph
• grid graph ∩ maximum degree 3
• gridline
• half-disk Helly
• hamiltonian
• hamiltonian ∩ planar
• harmonious
• 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 ∩ line ∩ perfect
• hereditary clique-Helly ∩ self-clique
• hereditary dismantlable
• hereditary dominating pair
• hereditary homogeneously orderable
• hereditary median
• hereditary modular
• hereditary perfect elimination bipartite
• hereditary weakly modular
• (hole,odd-cycle)-free
• hole-free ∩ planar
• homogeneously orderable
• homothetic triangle contact
• (house,hole,domino,sun)-free
• house-free ∩ weakly chordal
• hypercube
• induced-hereditary pseudo-modular
• intersection graphs of parallelograms (squares)
• 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-polygon
• k-regular, fixed k
• k-regular, fixed k>= 3
• k-regular, fixed k>= 6
• leaf power ∪ min leaf power
• line ∩ mock threshold
• line ∩ perfect
• line ∩ well covered
• line graphs of bipartite graphs
• line graphs of bipartite multigraphs
• line graphs of multigraphs without triangles
• line graphs of planar cubic bipartite graphs
• line graphs of triangle-free graphs
• line perfect
• linear domino
• linear domino ∩ maximum degree 4
• 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
• median
• median ∩ planar
• middle
• min leaf power
• mock threshold
• modular
• modular ∩ open-neighbourhood-Helly
• module-composed
• multitolerance
• murky
• nK₂-free, fixed n
• neighbourhood perfect
• neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
• normal Helly circular arc
• normal circular arc
• odd-signable
• odd-signable ∩ triangle-free
• opposition
• outer-string
• overlap
• (p,q)-colorable
• (p,q)-split
• p-connected
• p-tree
• pairwise compatibility
• parallelepiped
• partial 3d grid
• partial cube
• partial grid
• partitionable
• path orderable
• penny
• perfect connected-dominant
• perfect elimination bipartite
• permutation
• planar ∩ strongly regular
• polyhedral
• 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 proper interval
• probe strongly chordal
• probe unit interval
• proper Helly circular arc
• proper circular arc
• proper interval bigraph
• proper tolerance
• pseudo-median
• pseudo-median ∩ triangle-free
• pseudo-modular
• pseudo-modular ∩ triangle-free
• pseudo-split
• (q,t)
• quasi-brittle
• quasi-median
• quasitriangulated
• rectagraph
• reflexive
• relative neighbourhood graph
• self-clique
• self-complementary
• semi-median
• semi-square intersection
• semiperfectly orderable
• slightly triangulated
• solid grid graph
• solid triangular grid graph
• spider graph
• split-perfect
• star convex
• strict 2-threshold
• strict B₁-VCPG
• strong asteroid free
• strongly brittle
• strongly odd-signable
• strongly orderable
• strongly regular
• subtree filament
• subtree overlap
• sun-free ∩ weakly chordal
• superbrittle
• threshold signed
• threshold tolerance
• tolerance
• tolerance ∩ triangle-free
• trapezoepiped
• trapezoid
• tree convex
• tree-perfect
• triad convex
• triangular grid graph
• unbreakable
• unigraph
• unit Helly circle
• unit Helly circular arc
• unit bar visibility
• unit circular arc
• unit disk
• unit grid intersection
• unit interval bigraph
• unit square
• unit tolerance
• universally signable
• visibility
• walk regular
• weak bipolarizable
• weak dominating pair
• weakly bridged
• weakly median
• weakly modular
• well covered
• well-dominated
• wing-triangulated