Clique cover problem

(0,2)-colorable
(0,2)-graph ∩ bipartite
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
1-bounded bipartite
(2,0)-colorable
(2,2)-colorable ∩ chordal
2-bounded bipartite
2-connected ∩ (4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
2-outerplanar
2-split ∩ perfect
2-subdivision
2-subdivision ∩ planar
2-terminal series-parallel
2-threshold
2-tree
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
(2K₂,5K₁,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,C₄,C₅,S₃,co-rising sun,net)-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,S₃,X₁₅₉,X₁₆₀,X₁₆₁,X₁₆₂,X₄₆,X₇₀,2P₃,3K₂,H,P₂ ∪ P₄,X₁,co-rising sun,house,net)-free
(2K₂,C₅,triangle)-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,C₆,C₈,K_1,4,odd anti-cycle)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,odd anti-hole)-free
2K₂-free ∩ bipartite
2K₂-free ∩ probe cograph
2K₂-free ∩ probe trivially perfect
(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
(2K₃,2P₃,C_n+4,K₃ ∪ P₃)-free
(2K₃,3K₁,A,H,X₄₅)-free
(2K₃,C_n+4)-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
(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-leaf power
3-tree
3-tree ∩ planar
(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
(3K₁,2P₃)-free
(3K₁,3K₂)-free
(3K₁,E)-free
(3K₁,H)-free
(3K₁,K₂ ∪ claw)-free
(3K₁,P₂ ∪ P₄)-free
(3K₁,P₆)-free
(3K₁,X₁₇₂)-free
(3K₁,XC₁₂)-free
(3K₁,co-cross)-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,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,C₆,P₇,X₁₆₄,X₁₆₅,odd-cycle,sunlet₄)-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
3d grid
(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
(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,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-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
(6,1)-chordal ∩ bipartite
(6,2)
(6,2)-chordal ∩ bipartite
(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,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,T₂,odd-cycle)-free
(A,3P₃,C_n+4,P₃ ∪ P₄,X₁₀₂,X₁₈₀,X₁₈₁,X₁₈₂,X₁₈₃,house)-free
AC
AT-free ∩ bipartite
Apollonian network
B₀-VPG ∩ bipartite
B₀-VPG ∩ chordal
B₀-VPG ∩ strongly chordal
B₀-VPG ∩ triangle-free
B₁-CPG ∩ triangle-free
(BW₃,C₅,K_3,4,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃,triangle)-free
BW₃-free ∩ modular
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,C₆,C₈,K_1,4,odd-cycle)-free
(C₄,C₆,C₈,K_1,4,odd-cycle)-free ∩ planar
(C₄,C₆,odd-cycle)-free
(C₄,P₅)-free
(C₄,odd-hole)-free
(C₄,triangle)-free
(C₄,triangle)-free ∩ planar
C₄-free ∩ C₆-free ∩ bipartite
C₄-free ∩ induced-hereditary pseudo-modular
C₄-free ∩ perfect
(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,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,S₃,P,co-fork,fork,house,net)-free
(C₅,P,P₅,P,co-fork,fork,house)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,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,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-butterfly,co-diamond,triangle)-free
(C₅,co-gem,gem)-free
(C₅,co-gem,house)-free
C₅-free ∩ P₄-extendible
C₅-free ∩ P₄-tidy
C₅-free ∩ matrogenic
(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,triangle)-free
C₆-free ∩ modular
(C_n+3 ∪ K₁,diamond,paw)-free
(C_n+4,H)-free
(C_n+4,K₄)-free
(C_n+4,P₅,claw,gem)-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,X₁₀₂,X₂₀₄,P₃ ∪ 2K₁,gem)-free
(C_n+4,X₅₉,longhorn)-free
(C_n+4,XF₁²ⁿ⁺³,XF₆²ⁿ⁺²,X₃₄,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,K₃ ∪ 3K₁,dart,gem)-free
(C_n+4,bull,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
(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,odd-cycle)-free
D
Dilworth 2
Dilworth 3
Dilworth 4
(E,odd-cycle)-free
(E,triangle)-free
E-free ∩ bipartite
EPT ∩ chordal
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
Halin
Helly cactus subtree ∩ perfect
Helly chordal
Helly chordal ∩ clique-chordal
Hilbertian
H_n,q grid
(K_1,4,odd-cycle)-free
(K_1,4,odd-cycle)-free ∩ planar
(K_1,4,paw)-free
(K_1,5,triangle)-free
(K₂ ∪ K₃,P₄,butterfly)-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,X₁₆₃,X₉₅,co-diamond,house)-free
(K₂ ∪ claw,triangle)-free
(K_2,3,K₄)-minor-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
K_2,3-free ∩ hereditary modular
(K₃ ∪ 3K₁,C_n+4,co-dart,co-gem)-free
(K_3,3,3,C_n+4)-free
(K_3,3,K_3,3+e,2P₃,C_n+4)-free
(K_3,3,C_n+4)-free
(K₄,P₄)-free
(K₄,S₃,X₃₆,C₇,X₁₇₅,X₁₇₆,X₄₂,antenna,co-claw,net,odd-hole)-free
(K₄,odd anti-hole,odd-hole)-free
(K₄,odd anti-hole,odd-hole)-free ∩ dually chordal
K₄-free ∩ dually chordal ∩ perfect
K₄-free ∩ perfect
K₄-minor-free
(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
(K₅,X₁₂₆,X₁₇₄,3K₂)-minor-free
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-gem,house)-free
(P₂ ∪ P₄,triangle)-free
(P₃ ∪ 2K₁,C_n+4,X₁₀₂,X₂₀₄,co-gem)-free
(P₄,2P₃)-free
(P₄,triangle)-free
P₄-brittle
P₄-comparability
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,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,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,diamond)-free
(P₅,fork,house)-free
(P₅,gem)-free
(P₅,triangle)-free
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 ∩ chordal bipartite
(P₇,odd-cycle,star_1,2,3,sunlet₄)-free
(P₇,odd-cycle,star_1,2,3)-free
(P₇,odd-cycle)-free
P₇-free ∩ bipartite
PI
PI^*
PURE-2-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
(S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-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,net)-free ∩ chordal
(S₃,net)-free ∩ extended P₄-sparse
(S₃,net)-free ∩ split
S₃-free ∩ chordal
SC 2-tree
SC 3-tree
SC k-tree, fixed k
(T₂,X₂,X₃,hole,triangle)-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even-hole,odd-cycle)-free
V-perfect
(W₄,claw,gem,odd-hole)-free
(W₄,gem)-free ∩ short-chorded
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
(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
(X₃₄,X₃₆,XF₂ⁿ⁺¹,XF₃ⁿ,C_n+4,co-XF₁²ⁿ⁺³,co-XF₆²ⁿ⁺²)-free
(X₇₉,X₈₀)-free ∩ modular
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
(XC₁₁,odd-cycle)-free
(XC₁₁,odd-cycle)-free ∩ planar
(XC₁₂,triangle)-free
(XC₁₂,triangle)-free ∩ planar
(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
(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
(XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉,XZ₁₁,XZ₁₂,XZ₁₃,XZ₁₄,XZ₆,XZ₇,XZ₈,XZ₉)-free
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(G)-perfect
(3K₂,odd-hole,paw)-free
(A,T₂,odd anti-cycle)-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-paw)-free
(K_1,4,odd anti-cycle)-free
(P,butterfly,fork,gem)-free
(P,fork,gem)-free
(P,fork,house)-free
(P₃,triangle)-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
(W₄,co-claw,co-gem,odd anti-hole)-free
(X₁₇₇,odd anti-cycle)-free
(X₃₇,co-diamond,even anti-cycle)-free
(XC₁₁,odd anti-cycle)-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
absolutely perfect
absorbantly perfect
almost CIS
almost median
almost tree (1)
almost-split
alternately colourable
alternately orientable
alternately orientable ∩ co-comparability
(anti-hole,bull,odd-hole)-free
(anti-hole,co-domino,odd anti-cycle)-free
(anti-hole,co-sun,hole)-free
(anti-hole,hole,sun)-free
(anti-hole,hole)-free
(anti-hole,odd anti-cycle)-free
(anti-hole,odd-hole)-free
b-perfect ∩ chordal
balanced ∩ chordal
balanced ∩ co-line
balanced ∩ line
balanced ∩ paw-free
basic 4-leaf power
basic perfect
bi-cograph
biclique separable
biclique-Helly
biconvex
binary Hamming
bip^*
bipartable
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ claw-free
bipartite ∩ co-comparability
bipartite ∩ co-perfectly orderable
bipartite ∩ co-trapezoid
bipartite ∩ convex-round
bipartite ∩ cubic ∩ planar
bipartite ∩ distance-hereditary
bipartite ∩ girth >=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ grid intersection
bipartite ∩ maximum degree 3
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ mock threshold
bipartite ∩ module-composed
bipartite ∩ planar
bipartite ∩ probe interval
bipartite ∩ quasi-median
bipartite ∩ tolerance
bipartite ∩ trapezoid
bipartite ∩ unit grid intersection
bipartite ∩ weakly chordal
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
bipartite chain
bipartite permutation
bipartite tolerance
bipolarizable
bisplit
bisplit ∩ triangle-free
bithreshold
bitolerance
block
block duplicate
bounded bitolerance
bounded multitolerance
bounded tolerance
boxicity 2 ∩ co-bipartite
brittle
(bull,co-fork,co-gem)-free
(bull,co-fork,fork)-free
(bull,co-gem,gem)-free
(bull,fork,gem)-free
(bull,fork,house)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,odd anti-hole,odd-hole)-free
bull-free ∩ perfect
cactus
charming
chordal
chordal ∩ (claw,net)-free
chordal ∩ claw-free
chordal ∩ clique-Helly
chordal ∩ clique-chordal
chordal ∩ co-chordal
chordal ∩ 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 ∩ hamiltonian ∩ planar
chordal ∩ hereditary clique-Helly
chordal ∩ irredundance perfect
chordal ∩ maximal planar
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ planar
chordal ∩ probe diamond-free
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∪ co-chordal
chordal bipartite
chordal-perfect
circle graph with equator
circular convex bipartite
circular permutation
(claw ∪ 3K₁,odd-cycle)-free
(claw,co-claw)-free
(claw,diamond,odd-hole)-free
(claw,odd anti-hole,odd-hole)-free
(claw,odd-cycle)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free ∩ mock threshold
claw-free ∩ odd-hole-free ∩ tripartite
claw-free ∩ perfect
clique separable
clique-perfect ∩ triangle-free
cliquewidth 2
cliquewidth 3
cliquewidth 4
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-β-perfect
co-biclique separable
co-bipartite
co-bithreshold
co-bithreshold ∩ split
co-bounded tolerance
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-circular perfect
(co-claw,co-diamond,odd anti-hole)-free
(co-claw,co-paw)-free
(co-claw,odd anti-cycle)-free
(co-claw,odd anti-hole,odd-hole)-free
co-cluster
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 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-forest-perfect
(co-fork,odd anti-cycle)-free
(co-gem,gem)-free
(co-gem,house)-free
co-interval
co-interval ∩ cograph
co-interval ∪ interval
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-perfectly orderable
co-probe cograph
co-strongly chordal
co-threshold tolerance
co-tolerance
co-trapezoid
co-trivially perfect
co-unipolar
co-unipolar ∪ unipolar
cograph
cograph contraction
comparability
comparability ∩ distance-hereditary
comparability ∩ split
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
comparability graphs of series-parallel posets
complete bipartite
complete multipartite
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex
(cross,triangle)-free
cubical
cycle-bicolorable
d-trapezoid
(diamond,odd-hole)-free
diamond-free ∩ perfect
difference
directed path
distance-hereditary
domination
domination perfect ∩ triangle-free
(domino,gem,hole,house,net)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free ∩ modular
domishold
double split
doubled
doubly chordal
dually chordal ∩ tripartite
even-hole-free ∩ probe chordal
extended P₄-reducible
extended P₄-sparse
forest-perfect
(fork,odd-cycle)-free
(fork,triangle)-free
generalized split
generalized strongly chordal
girth >=9
good
grid
grid graph
grid graph ∩ maximum degree 3
gridline
half
half-disk Helly
hamiltonian ∩ split
hereditary Helly
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 biclique-Helly
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary disk-Helly
hereditary dually chordal
hereditary homogeneously orderable
hereditary median
hereditary modular
hereditary open-neighbourhood-Helly
hereditary perfect elimination bipartite
hereditary sat
(hole,odd anti-hole)-free
(hole,odd-cycle)-free
hole-free ∩ planar
(house,hole,domino,sun)-free
house-free ∩ weakly chordal
hypercube
i-triangulated
independent module-composed
intersection graphs of parallelograms (squares)
interval bigraph
interval containment bigraph
isometric subgraph of a hypercube
k-outerplanar
k-path graph, fixed k
k-starlike
k-tree, fixed k
kernel solvable
leaf power
leaf power ∩ min leaf power
leaf power ∪ min leaf power
line ∩ mock threshold
line ∩ perfect
line graphs of acyclic multigraphs
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of planar cubic bipartite graphs
linear cliquewidth 2
locally perfect
matrogenic
matroidal
maxibrittle
maximal outerplanar
maximum degree 3 ∩ planar ∩ triangle-free
median
median ∩ planar
min leaf power
minimally imperfect
mock threshold
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
module-composed
multitolerance
murky
neighbourhood perfect
neighbourhood-Helly ∩ triangle-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-cycle-free
(odd-hole,paw)-free
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable ∩ triangle-free
open-neighbourhood-Helly
opposition
outerplanar
parallelepiped
parity
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 3d grid
partial 4-tree
partial cube
partial grid
partial k-tree, fixed k
partner-limited
paw-free
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
permutation
planar ∩ triangle-free
power-chordal
premedian
preperfect
probe Gallai
probe HHDS-free
probe Meyniel
probe P₄-reducible
probe P₄-sparse
probe bipartite chain
probe bipartite distance-hereditary
probe block
probe chordal
probe chordal ∩ weakly chordal
probe chordal bipartite
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe distance-hereditary
probe interval
probe interval bigraph
probe proper interval
probe ptolemaic
probe split
probe strongly chordal
probe threshold
probe trivially perfect
probe unit interval
proper interval bigraph
proper tolerance
pseudo-median ∩ triangle-free
pseudo-modular ∩ triangle-free
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
quasi-Meyniel
quasi-brittle
quasi-parity
quasitriangulated
rectagraph
restricted block duplicate
rigid circuit
rooted directed path
semi-P₄-sparse
semi-median
semiperfectly orderable
series-parallel
short-chorded
skeletal
slender
slightly triangulated
slim
solid grid graph
split
split ∩ strongly chordal
split ∩ superperfect
split-perfect
square of tree
star convex
strict 2-threshold
strict quasi-parity
strictly chordal
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly orderable
strongly perfect
sun-free ∩ weakly chordal
superbrittle
superperfect
thick tree
threshold signed
threshold tolerance
tolerance
tolerance ∩ triangle-free
totally unimodular
trapezoepiped
trapezoid
tree convex
tree-cograph
tree-perfect
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
triangle-free
triangulated
undirected path
unicyclic
unimodular
unipolar
unit interval bigraph
unit tolerance
very strongly perfect
weak bipolarizable
weakly chordal
wing-triangulated

Input:	A graph G in this class and an integer k.
Output:	True iff the vertices of G can be partitioned into k sets S_i, such that whenever two vertices are in the same set S_i, they are adjacent.

Problem: Clique cover

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI