Weighted clique problem

(0,2)-graph
(0,3)-colorable
(1,1)-colorable
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-DIR
1-bounded tripartite
(2,0)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
2-connected ∩ (4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-split
2-split ∩ perfect
2-strongly regular ∩ planar
2-subdivision
2-subdivision ∩ planar
2-threshold
(2K₂,4K₁,co-claw,co-diamond)-free
(2K₂,C₄,C₅,S₃,net,rising sun)-free
(2K₂,C₄,C₅,S₃,net)-free
(2K₂,C₄,C₅,claw,diamond)-free
(2K₂,C₄,C₅,co-claw,co-diamond)-free
(2K₂,C₄,C₅,co-sun)-free
(2K₂,C₄,C₅,sun)-free
(2K₂,C₄,C₅)-free
(2K₂,C₄)-free
(2K₂,C₅,C₆,C₇,C₈,XC₁₁,co-claw,co-diamond)-free
(2K₂,C₅,T₂)-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,co-claw,co-diamond)-free
(2K₂,house)-free
(2K₂,odd anti-hole)-free
2K₂-free ∩ probe cograph
(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,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 + e,X₉₈,house)-free
(2K₃ + e,X₉₉,house)-free
(2K₃ + e,house)-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
(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,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
(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,butterfly,diamond)-free
(3K₁,K₂ ∪ claw)-free
(3K₁,P₆)-free
(3K₁,X₁₇₂)-free
(3K₁,co-fork)-free
(3K₁,house)-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,P₂ ∪ P₄,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,net)-free
(3K₂,E,P₂ ∪ P₄,net,odd anti-hole,odd-hole)-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-colorable
(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
4-leaf power
4-regular
4-regular ∩ hamiltonian
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(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,C_n+4)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,gem)-free
(4K₁,house)-free
(4K₁,odd anti-hole,odd-hole)-free
(5,1)
(5,2)-chordal
(5,2)-crossing-chordal
(5,2)-odd-chordal
(5,2)-odd-crossing-chordal
(5,2)-odd-noncrossing-chordal
5-colorable
5-leaf power
5-leaf power ∩ distance-hereditary
(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-colorable
(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)
(7,4)
(8,4)
(9,6)
(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,H,K_3,3,X₄₅,triangle)-free
(A,P₆,clique wheel,domino,hole,house)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AC
AT-free ∩ chordal
B₀-CPG
B₀-VPG ∩ chordal
B₀-VPG ∩ strongly chordal
B₀-VPG ∩ triangle-free
B₁-CPG
B₁-CPG ∩ triangle-free
B₁-VCPG
(BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-free
Berge
Berge ∩ bull-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,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,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
(C₄,C₅,C₆,C₇,C₈)-free ∩ maximum degree 3 ∩ planar
(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,K₄,claw,diamond)-free
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,S₃)-free
(C₄,X₉₁,claw)-free
(C₄,A,H)-free
(C₄,claw,diamond)-free
(C₄,co-claw)-free
(C₄,diamond)-free
(C₄,odd-hole)-free
(C₄,triangle)-free
(C₄,triangle)-free ∩ planar
C₄-free
C₄-free ∩ co-comparability
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,C₆,X₁₆₄,X₁₆₅,sunlet₄,triangle)-free
(C₅,K₂ ∪ K₃,K_2,3,P,P₂ ∪ P₃,P₅,P,P₂ ∪ P₃,co-fork,fork,house)-free
(C₅,K_3,3-e,T₂,X₁₈,X₉₄,domino,triangle)-free
(C₅,P,P₅,P,co-fork,fork,house)-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,P₆,P₆)-free
(C₅,S₃,X₁₁,3K₂,C₇,P₂ ∪ P₄,X₁₇₃)-free ∩ co-line
(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,bull,co-gem,gem)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-free
(C₅,house)-free
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,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,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,house)-free
(C₆,triangle)-free
CPG
(C_n+3 ∪ K₁,diamond,paw)-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,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,odd-cycle ∪ K₁,even anti-hole,net)-free
(C_n+4,H)-free
(C_n+4,P₅,claw,gem)-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,X₃₁,XF₂ⁿ⁺¹,XF₃ⁿ)-free
(C_n+4,T₂,XF₂ⁿ⁺¹)-free
(C_n+4,T₂,net)-free
(C_n+4,X₁₀₂,X₂₀₄,P₃ ∪ 2K₁,gem)-free
(C_n+4,X₅₉,longhorn)-free
(C_n+4,K₃ ∪ 3K₁,dart,gem)-free
(C_n+4,claw,gem)-free
(C_n+4,claw,net)-free
(C_n+4,claw)-free
(C_n+4,dart,gem)-free
(C_n+4,diamond)-free
(C_n+4,gem)-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,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
D
Delaunay
Dilworth 3
Dilworth 4
(E,triangle)-free
E-free ∩ planar
EPT ∩ chordal
F_n grid
Gabriel
Gallai
Gallai-perfect
(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
HHDA-free
HHDG-free
HHDS-free
HHDbicycle-free
HHG-free
HHP-free
Helly ∩ bridged
Helly cactus subtree ∩ perfect
Helly chordal
Helly chordal ∩ clique-chordal
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
H_n,q grid
(K_1,4,diamond)-free
(K_1,4,paw)-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,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,house)-free
(K₂ ∪ claw,triangle)-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
(K_2,3,X₃₇,X₃₈,diamond,domino,house,twin-C₅)-free
(K_2,3,diamond)-free
(K_2,3,diamond)-free ∩ weakly modular
(K₃ ∪ 3K₁,C_n+4,co-dart,co-gem)-free
(K₃ ∪ P₃,C₆,P,P₇,X₃₇,X₄₁)-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,K₅)-minor-free
(K_3,3,C_n+4)-free
(K₄,P₅,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉)-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,co-gem)-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,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
K₆-free
K₇-free
Laman
Laman ∩ planar
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
Mycielski
N^*-perfect
(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,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
(P₂ ∪ P₃,house)-free
(P₂ ∪ P₄,triangle)-free
(P₃ ∪ 2K₁,C_n+4,X₁₀₂,X₂₀₄,co-gem)-free
P₄-brittle
P₄-comparability
P₄-extendible
P₄-indifference
P₄-laden
P₄-lite
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,anti-hole,co-domino,co-gem)-free
(P₅,A,P₆,anti clique wheel,anti-hole,co-domino)-free
(P₅,A,anti-hole,co-domino)-free
(P₅,C₆)-free ∩ weakly chordal
(P₅,P,anti-hole)-free
(P₅,P,gem)-free
(P₅,P₂ ∪ P₃)-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,co-fork,house)-free
(P₅,co-fork)-free
(P₅,diamond)-free
(P₅,fork,house)-free
(P₅,gem)-free
(P₅,house)-free
(P₅,triangle)-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,triangle)-free
P₆-free ∩ tripartite
PI
PI^*
PURE-3-DIR
(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
(S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
(S₃,3K₂,E,P₂ ∪ P₄)-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)-free
(S₃,C_n+4,net)-free
(S₃,C_n+6,X₃₇,antenna,co-claw,co-sun)-free
(S₃,co-claw,net)-free
(S₃,co-claw)-free
(S₃,net)-free ∩ chordal
(S₃,net)-free ∩ extended P₄-sparse
(S₃,net)-free ∩ split
S₃-free ∩ chordal
Urquhart
V-perfect
W_2n+3-free
(W₄,W₅,butterfly)-free
(W₄,claw,gem,odd-hole)-free
(W₄,claw,gem)-free
(W₄,claw)-free
(W₄,gem)-free
(W₄,gem)-free ∩ short-chorded
Welsh-Powell opposition
Welsh-Powell perfect
(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
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₃₇,diamond,even-cycle)-free
(X₃₈,gem,house)-free
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free ∩ normal circular arc ∩ quasi-line
XC₁₀-free
XC₁₀-free ∩ pseudo-modular
XC₁₀-free ∩ weakly modular
(XC₁₁,claw,diamond)-free
(XC₁₂,triangle)-free
(XC₁₂,triangle)-free ∩ planar
XC₁₃-free
(XC₇,XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₈)-free
XC₉-free
(XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-free
β-perfect
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(G)-perfect
(3K₂,C₆,P₇,X₁₆₄,X₁₆₅,sunlet₄,odd anti-cycle)-free
(A,P₆,co-domino)-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,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,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,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,odd anti-cycle)-free
(K_1,4,P,co-fork,house)-free
(K_1,4,house)-free
(K_1,4,odd anti-cycle)-free
K₂ ∪ claw-free
(P,P₇)-free
(P,butterfly,fork,gem)-free
(P,fork,gem)-free
(P,fork,house)-free
(P,house)-free
(P₆,X₃₀,X₈)-free
(P₆,co-claw)-free
P₆-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
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-free
(W₄,co-claw,co-gem,odd anti-hole)-free
(W₄,co-claw,co-gem)-free
(W₄,co-claw)-free
(X₁₇₇,odd anti-cycle)-free
(X₈₂,X₈₃,house)-free
(X₉₁,co-claw)-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
(XC₁₂,co-cycle)-free
(claw ∪ 3K₁,odd anti-cycle)-free
(n+4)-pan-free
odd-cycle ∪ K₁-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
absolutely perfect
absorbantly perfect
almost CIS
almost-split
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
alternation
(anti-hole,bull,odd-hole)-free
(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
(anti-hole,odd-hole)-free
apex
b-perfect
b-perfect ∩ chordal
balanced
balanced ∩ chordal
balanced ∩ co-line
balanced ∩ line
bar visibility
basic 4-leaf power
basic perfect
biclique separable
biclique-Helly
bip^*
bipartable
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
bipolarizable
bithreshold
bitolerance
block
block duplicate
book thickness 2
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 1
boxicity 2 ∩ co-bipartite
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,hole,odd anti-hole)-free
(bull,house)-free
(bull,odd anti-hole,odd-hole)-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 ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ dominating pair
chordal ∩ domination perfect
chordal ∩ domino
chordal ∩ dually chordal
chordal ∩ gem-free
chordal ∩ hamiltonian
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ probe diamond-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal-perfect
circle
circle ∩ diamond-free
circle-n-gon, fixed n
circle-polygon
circle-trapezoid
circular arc
circular arc ∩ clique-Helly
circular arc ∩ co-bipartite
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular strip
(claw,co-claw)-free
(claw,diamond,odd-hole)-free
(claw,diamond)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd anti-hole)-free
(claw,odd anti-hole)-free ∩ tripartite
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ mock threshold
claw-free ∩ odd anti-hole-free ∩ tripartite
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
clique separable
clique-perfect ∩ triangle-free
cliquewidth 3
cliquewidth 4
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-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bithreshold
(co-butterfly,co-claw)-free
co-chordal
(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,odd anti-hole)-free
(co-claw,odd-hole)-free
co-claw-free
co-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 2
co-comparability graphs of posets of interval dimension d
(co-cricket,house)-free
co-cycle-free
(co-diamond,diamond)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-forest-perfect
(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-interval ∪ interval
co-interval bigraph
co-interval containment bigraph
co-interval filament
co-interval mixed
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,paw)-free
(co-paw,triangle)-free
co-perfectly orderable
co-probe cograph
co-quasi-line
co-strongly chordal
co-threshold tolerance
co-tolerance
co-unipolar
co-unipolar ∪ unipolar
cograph contraction
coin
complete Hamming
concave-round
convex-round
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cycle-bicolorable
d-trapezoid
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
directed path
disk contact
distance-hereditary
domination
domination perfect ∩ planar
domination perfect ∩ triangle-free
domino
(domino,gem,house)-free
(domino,gem,house)-free ∩ pseudo-modular
double split
doubled
doubly chordal
dually chordal ∩ tripartite
even-cycle-free
even-hole-free ∩ probe chordal
extended P₄-laden
extended P₄-reducible
extended P₄-sparse
forest-perfect
(fork,house)-free
(fork,triangle)-free
fuzzy circular interval
fuzzy linear interval
gem-free
generalized split
generalized strongly chordal
generically minimally rigid
genus 0
genus 1
geodetic
girth >=9
good
gridline
hamiltonian ∩ interval
hamiltonian ∩ planar
hamiltonian ∩ split
hereditary Helly
hereditary Matula perfect
hereditary N^*-perfect
hereditary V-perfect
hereditary Welsh-Powell opposition
hereditary Welsh-Powell perfect
hereditary biclique-Helly
hereditary clique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ self-clique
hereditary disk-Helly
hereditary dismantlable
hereditary dually chordal
hereditary homogeneously orderable
hereditary maximal clique irreducible
hereditary neighbourhood-Helly
hereditary open-neighbourhood-Helly
hereditary sat
(hole,odd anti-hole)-free
hole-free ∩ planar
homothetic triangle contact
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
i-triangulated
intersection graphs of parallelograms (squares)
interval
interval filament
k-polygon
k-starlike
kernel solvable
leaf power
leaf power ∩ min leaf power
leaf power ∪ min leaf power
line
line ∩ mock threshold
line ∩ perfect
line ∩ well covered
line graphs of acyclic multigraphs
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 arboricity <= 2
linear domino
linear domino ∩ maximum degree 4
linearly convex triangular grid graph
locally bipartite
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
locally perfect
locally split
matrogenic
matroidal
max-tolerance
maxibrittle
maximal clique irreducible
maximal planar
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
min leaf power
minimally imperfect
mock threshold
mock threshold ∩ split
module-composed
monopolar
multitolerance
murky
nearly bipartite
neighbourhood perfect
neighbourhood-Helly ∩ triangle-free
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
(odd building,odd-hole)-free
odd-cycle ∪ K₁-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable ∩ triangle-free
open-neighbourhood-Helly
opposition
overlap
parallelepiped
parity
partial bar visibility
partial rectangle visibility
partner-limited
paw-free
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfectly 1-transversable
perfectly contractile
perfectly orderable
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
power-chordal
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P₄-reducible
probe P₄-sparse
probe bipartite distance-hereditary
probe block
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe proper interval
probe ptolemaic
probe split
probe strongly chordal
probe trivially perfect
probe unit interval
proper tolerance
pseudo-median
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-Meyniel
quasi-brittle
quasi-line
quasi-median
quasi-parity
quasitriangulated
rectagraph
rectangle visibility
relative neighbourhood graph
restricted block duplicate
rigid circuit
rooted directed path
semi-P₄-sparse
semi-square intersection
semiperfectly orderable
short-chorded
skeletal
slender
slightly triangulated
slim
solid triangular grid graph
spider graph
split
split ∩ strongly chordal
split-neighbourhood
split-perfect
square of tree
strict B₁-VCPG
strict quasi-parity
strictly chordal
strictly clique irreducible
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly even-signable
strongly odd-signable
strongly orderable
strongly perfect
subhamiltonian
sun-free ∩ weakly chordal
superbrittle
superperfect
thick tree
thickness <= 2
threshold tolerance
tolerance
toroidal
totally unimodular
trapezoepiped
trapezoid
tree-cograph
tree-perfect
triangle contact
triangle-free
triangular grid graph
triangulated
tripartite
undirected path
unimodular
unipolar
unit Helly circle
unit bar visibility
unit tolerance
very strongly perfect
weak bar visibility
weak bipolarizable
weak bisplit
weak rectangle visibility
weakly chordal
weakly geodetic
weakly median
wing-triangulated

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 pairwise adjacent vertices, such that the sum of the weights of the vertices in S is at least k.

Problem: Weighted clique

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI