Problem: Cochromatic colouring

Definition:

(decision variant)

Input:	A graph G in this class and an integer k.
Output:	True iff the vertices of G can be partitioned into at most k sets, such that each partite set induces either an independent set or a clique in G.

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI

(0,2)-colorable
(0,2)-colorable ∩ chordal
(0,2)-graph
(0,2)-graph ∩ bipartite
(0,3)-colorable
(0,3)-colorable ∩ chordal
(1,1)-colorable
(1,2)-colorable
(1,2)-colorable ∩ chordal
(1,2)-polar
(1,2)-polar ∩ chordal
(1,2)-split
1-DIR
1-bounded bipartite
1-bounded tripartite
1-string
(2,0)-colorable
(2,0)-colorable ∩ chordal
(2,1)-colorable
(2,2)-colorable
(2,2)-colorable ∩ chordal
(2,2)-interval
2-DIR
2-SEG
2-bounded bipartite
2-circular arc
2-circular track
2-connected
2-connected ∩ (4-fan,C_n+4,K₅ - e,S₃,H,K₃ ∪ 2K₁)-free
2-connected ∩ (P₆,claw)-free
2-connected ∩ cubic ∩ planar
2-connected ∩ linearly convex triangular grid graph
2-edge-connected
2-interval
2-leaf power
2-outerplanar
2-split
2-split ∩ perfect
2-strongly regular
2-strongly regular ∩ planar
2-subdivision
2-subdivision ∩ planar
2-terminal series-parallel
2-thin
2-threshold
2-track
2-tree
2-tree ∩ probe interval
(2C₄,3K₂,C₆,E,P₂ ∪ P₄,P₆,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,odd-cycle)-free
2K₁-free
(2K₂,3K₁,C₄,P₄)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,K_1,4,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈,H,X₈₅)-free
(2K₂,3K₁,C₅,C₆,C₇,C₈)-free
(2K₂,3K₁,P₃)-free
(2K₂,3K₁)-free
(2K₂,4K₁,C₅,co-diamond)-free
(2K₂,4K₁,co-claw,co-diamond)-free
(2K₂,5K₁,C₅,K₃ ∪ 2K₁,P₃ ∪ 2K₁,C₆,C₇,C₈,K_1,4,K₅ - e,claw ∪ K₁,co-butterfly,co-cricket,co-dart,co-gem)-free
(2K₂,A,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,C₅,H,S₃,X₁₆₀,X₁₅₉,net,rising sun)-free
(2K₂,C₄,C₅,S₃,X₁₅₉,X₁₆₀,H,co-rising sun,net)-free
(2K₂,C₄,C₅,S₃,claw,net)-free
(2K₂,C₄,C₅,S₃,co-claw,net)-free
(2K₂,C₄,C₅,S₃,co-rising sun,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,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,P₄,triangle)-free
(2K₂,C₄,P₄)-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,C₆,C₇,C₈,XC₁₁,co-claw,co-diamond)-free
(2K₂,C₅,C₆,C₇,C₈)-free
(2K₂,C₅,C₆,net)-free
(2K₂,C₅,T₂)-free
(2K₂,C₅,triangle)-free
(2K₂,C₅)-free
(2K₂,K_3,3,K_3,3+e,P₄,2P₃)-free
(2K₂,P₃,triangle)-free
(2K₂,P₃)-free
(2K₂,P₄,2P₃)-free
(2K₂,P₄,co-dart)-free
(2K₂,P₄,co-diamond,co-paw)-free
(2K₂,P₄)-free
(2K₂,2P₃,C₆)-free
(2K₂,C₆,C₈,K_1,4,odd anti-cycle)-free
(2K₂,C₆,odd anti-cycle)-free
(2K₂,P₆)-free
(2K₂,X₉₁,co-claw)-free
(2K₂,claw)-free
(2K₂,co-claw,co-diamond)-free
(2K₂,co-diamond)-free
(2K₂,house)-free
(2K₂,net)-free
(2K₂,odd anti-hole)-free
2K₂-free
2K₂-free ∩ bipartite
2K₂-free ∩ probe cograph
2K₂-free ∩ probe trivially perfect
(2K₃ + e,3K₁,C₅,T₂,X₁₈,X₉₄,co-domino)-free
(2K₃ + e,5-pan,A,C₆,E,K_3,3-e,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,5-pan,A,C₆,E,P₆,R,X₁₆₆,X₁₆₇,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₃₇,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₈,antenna,co-antenna,co-domino,co-fish,co-twin-C₅,co-twin-house,domino,fish,twin-C₅,twin-house)-free
(2K₃ + e,A,C₅,C₆,E,H,K_3,3-e,P₆,R,S₃,X₁₆₆,X₁₆₇,X₁₆₈,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₆,X₉₈,A,C₆,E,H,P₆,R,X₁₆₆,X₁₆₇,X₁₆₈,X₁₆₉,X₁₇₀,X₁₇₁,X₁₇₂,X₁₈,X₄₅,X₅,X₅₈,X₈₄,X₉₅,X₉₆,X₉₈,antenna,co-antenna,co-cross,co-domino,co-fish,co-twin-house,cross,domino,fish,net,twin-house)-free
(2K₃ + e,A,C₅,C₆,E,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
(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
(2K₃,2K₃ + 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,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,C₅,P₅,X₁₇₀,A)-free
(2P₃,C₄,C₆)-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-DIR
3-DIR contact
3-Helly
3-circular track
3-interval
3-leaf power
3-mino
3-track
3-tree
3-tree ∩ planar
(3K₁,C₄,C₅)-free
(3K₁,C₄,P₃)-free
(3K₁,C₅,K₃ ∪ K₄,BW₃,K_3,4-e,T₂,X₁₈,X₉₂,X₉₃)-free
(3K₁,C₅,K₅ - e,C₆ ∪ K₁,C₇,K_3,3 ∪ K₁,K_3,3-e ∪ K₁,domino ∪ K₁)-free
(3K₁,C₅,C₆,P₆)-free
(3K₁,C₅,C₆,X₁₆₄,X₁₆₅,sunlet₄)-free
(3K₁,C₅,butterfly,diamond)-free
(3K₁,P₃)-free
(3K₁,P₄)-free
(3K₁,2P₃)-free
(3K₁,3K₂)-free
(3K₁,C₆)-free
(3K₁,E)-free
(3K₁,H)-free
(3K₁,K_1,5)-free
(3K₁,K₂ ∪ claw)-free
(3K₁,P₂ ∪ P₄)-free
(3K₁,P₃)-free
(3K₁,P₆)-free
(3K₁,T₂,X₂,X₃,anti-hole)-free
(3K₁,X₁₇₂)-free
(3K₁,XC₁₂)-free
(3K₁,co-cross)-free
(3K₁,co-fork)-free
(3K₁,house)-free
(3K₁,paw)-free
3K₁-free
(3K₂,A,C₄ ∪ 2K₁,E,P₂ ∪ P₃,R,K₅ - e,co-claw,net,odd anti-hole,twin-house)-free
(3K₂,C₄ ∪ P₂,C₅,C₆,K₂ ∪ K₃,K_3,3,K_3,3+e,P₂ ∪ P₄,P₆,X₁₈,X₅,2P₃,C₆,C₇,X₈₄,antenna,domino,fish)-free
(3K₂,C₄ ∪ P₂,C₅,P₂ ∪ P₄,P₅,S₃,X₁,X₄₆,X₇₀,3K₂,C₄ ∪ P₂,P₂ ∪ P₄,X₁,X₄₆,X₇₀,co-fish,co-rising sun,fish,house,net,rising sun)-free
(3K₂,C₅,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,odd anti-hole,odd-hole)-free
(3K₂,E,P₂ ∪ P₄,net)-free
(3K₂,E,net,odd anti-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
3d grid
(4,0)-colorable
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-fan,K_1,4,W₄,W₅,A ∪ K₁,co-fork ∪ K₁,gem ∪ K₁,net ∪ K₁)-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,P₄)-free
(4K₁,C_n+4)-free
(4K₁,co-claw,co-diamond)-free
(4K₁,gem)-free
(4K₁,house)-free
(4K₁,net)-free
(4K₁,odd anti-hole,odd-hole)-free
4K₁-free
(5,1)
(5,2)
(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
(5-pan,T₂,X₁₇₂)-free ∩ planar
5-regular
5-regular ∩ hamiltonian
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
5K₁-free
(6,1)-chordal
(6,1)-chordal ∩ bipartite
(6,1)-even-chordal
(6,2)
(6,2)-chordal
(6,2)-chordal ∩ bipartite
(6,3)
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
6K₁-free
(7,3)
(7,4)
(7,5)
7K₁-free
(8,4)
(9,6)
(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,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
AC
AT-free
AT-free ∩ bipartite
AT-free ∩ chordal
AT-free ∩ claw-free
Apollonian network
B₀-CPG
B₀-VPG
B₀-VPG ∩ bipartite
B₀-VPG ∩ chordal
B₀-VPG ∩ strongly chordal
B₀-VPG ∩ triangle-free
B₁-CPG
B₁-CPG ∩ triangle-free
B₁-VCPG
B₁-VPG
B₂-VPG
B₃-VPG
(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
Birkhoff
B_k-VPG
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,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,E,P₆,S₃,X₁₅₉,X₂₁₉,X₅₈,A,X₁₅₉,X₂₁₉,co-rising sun,net,rising sun)-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,C₈,K_1,4,odd-cycle)-free
(C₄,C₆,C₈,K_1,4,odd-cycle)-free ∩ planar
(C₄,C₆,odd-cycle)-free
(C₄,K₄,claw,diamond)-free
(C₄,P₄,dart)-free
(C₄,P₄,diamond,paw)-free
(C₄,P₄)-free
(C₄,P₅)-free
(C₄,P₆)-free
(C₄,S₃)-free
(C₄,X₉₁,claw)-free
(C₄,A,H)-free
(C₄,P₃,triangle)-free
(C₄,P₃)-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 ∩ C₆-free ∩ bipartite
C₄-free ∩ co-comparability
C₄-free ∩ galled-tree explainable
C₄-free ∩ induced-hereditary pseudo-modular
C₄-free ∩ odd-signable
C₄-free ∩ perfect
C₄-free ∩ weakly 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,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,bull,co-gem,fork)-free
(C₅,P,P₅,P,co-fork,fork,house)-free
(C₅,P,P₅,P,house)-free
(C₅,P,P₅,house)-free
(C₅,P,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,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
(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,house)-free
C₅-free
C₅-free ∩ P₄-extendible
C₅-free ∩ P₄-tidy
C₅-free ∩ matrogenic
(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
(C₆,C₆)-free murky
(C₆,house)-free
(C₆,triangle)-free
C₆-free
C₆-free ∩ modular
(C₇,odd anti-hole)-free
CIS
CONV
CPG
(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+4,H)-free
(C_n+4,K₄)-free
(C_n+4,P₅,bull)-free
(C_n+4,P₅,claw,gem)-free
(C_n+4,S₃ ∪ K₁,X₁₀₃,claw,eiffeltower,net ∪ K₁)-free
(C_n+4,S₃ ∪ K₁,claw,net)-free
(C_n+4,S₃,claw,net)-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,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,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
C_n+6-free
C_n+7-free
D
Delaunay
Deza
Dilworth 1
Dilworth 2
Dilworth 3
Dilworth 4
(E,P)-free
(E,odd-cycle)-free
(E,triangle)-free
E-free
E-free ∩ bipartite
E-free ∩ planar
EPT
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
Halin
Hamilton-connected
Hamiltonian hereditary
Hamming
Helly
Helly 2-acyclic subtree
Helly ∩ bridged
Helly ∩ reflexive
Helly cactus subtree
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
Helly subtree
Hilbertian
H_n,q grid
(K_1,4,P,P₅,fork)-free
(K_1,4,P₅)-free
(K_1,4,diamond)-free
(K_1,4,odd-cycle)-free
(K_1,4,odd-cycle)-free ∩ planar
(K_1,4,paw)-free
K_1,4-free
K_1,4-free ∩ almost claw-free ∩ locally connected
K_1,4-free ∩ well covered
(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,K₄)-minor-free
(K_2,3,P,P₅,X₁₆₃,X₉₅,diamond)-free
(K_2,3,P,P₅)-free
(K_2,3,P,hole)-free
(K_2,3,P₄,co-butterfly)-free
(K_2,3,P₅)-free
(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
K₂-free
(K₃ ∪ 2K₁,K₃ ∪ 2K₁,bull,co-cricket,co-dart,cricket,dart)-free
(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,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
K₃-minor-free
(K_4,4,P₅)-free
(K₄,P₄)-free
(K₄,P₅,W₅,X₁₉₄,X₈₆,X₈₈,X₈₉,X₉₀,C₇,X₁₉₅,X₁₉₆,X₃₈,X₃₉)-free
(K₄,P₅)-free
(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 ∩ map
K₄-free ∩ perfect
K₄-free ∩ planar
K₄-minor-free
(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
(K₅,X₁₂₆,X₁₇₄,3K₂)-minor-free
K₅-free
K₆-free
K₇-free
Laman
Laman ∩ planar
Matula perfect
Meyniel
Meyniel ∩ co-Meyniel
Meyniel ∩ weakly chordal
Mycielski
N^*
N^*-perfect
NLCT-width 1
(P,P₅,S₃,P,co-fork,fork,house,net)-free
(P,P₅,3K₂,gem)-free
(P,P₅,P,co-fork,fork,house)-free
(P,P₅,co-fork)-free
(P,P₅)-free
(P,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,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
(P₃ ∪ 2K₁,C_n+4,X₁₀₂,X₂₀₄,co-gem)-free
(P₃,triangle)-free
P₃-free
(P₄,2P₃)-free
(P₄,co-cycle)-free
(P₄,co-diamond,co-paw,diamond,paw)-free
(P₄,co-diamond,co-paw)-free
(P₄,cycle)-free
(P₄,diamond,paw)-free
(P₄,triangle)-free
P₄-bipartite
P₄-brittle
P₄-comparability
P₄-extendible
P₄-extendible ∩ P₄-sparse
P₄-free
P₄-free ∩ starlike
P₄-indifference
P₄-laden
P₄-lite
P₄-reducible
P₄-simplicial
P₄-sparse
P₄-tidy
P₄-tidy ∩ (S₃,3K₂,E,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
P₄-tidy ∩ balanced
P₄-tidy ∩ hereditary clique-Helly ∩ perfect
P₄-tidy ∩ perfect
(P₅,S₃,A,E,X₁,anti-hole,co-domino,co-rising sun,net)-free
(P₅,S₃,anti-hole,co-domino,co-gem)-free
(P₅,X₈₂,X₈₃)-free
(P₅,A,P₆,anti clique wheel,anti-hole,co-domino)-free
(P₅,A,anti-hole,co-domino)-free
(P₅,C₆)-free
(P₅,P,anti-hole)-free
(P₅,P,gem)-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-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,house)-free
(P₅,co-fork)-free
(P₅,cricket)-free
(P₅,diamond)-free
(P₅,fork,house)-free
(P₅,fork)-free
(P₅,gem)-free
(P₅,house)-free
(P₅,triangle)-free
P₅-free
P₅-free ∩ tripartite
P₅-free ∩ weakly chordal
(P₆,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₅,X₆,X₇,X₈,X₉,C₆,P₆,antenna,hole)-free
(P₆,X₃₀,X₈)-free
(P₆,claw)-free
(P₆,hole,house)-free
(P₆,house)-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,odd-cycle)-free
P₇-free
P₇-free ∩ bipartite
PI
PI^*
PURE-2-DIR
PURE-3-DIR
PURE-k-DIR
Raspail
(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,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,P₂ ∪ P₄,odd anti-hole,odd-hole)-free
(S₃,3K₂,E,P₂ ∪ P₄)-free
(S₃,3K₂,E,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,C_n+6,X₃₇,antenna,co-claw,co-sun)-free
(S₃,claw,net)-free
(S₃,claw,net)-free ∩ chordal
(S₃,co-claw,net)-free
(S₃,co-claw)-free
(S₃,net)-free
(S₃,net)-free ∩ chordal
(S₃,net)-free ∩ extended P₄-sparse
(S₃,net)-free ∩ split
(S₃,net)-free ∩ sun-free
S₃-free
S₃-free ∩ chordal
SC 2-tree
SC 3-tree
SC k-tree, fixed k
SEG
(T₂,X₂,X₃,hole,triangle)-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even-hole,odd-cycle)-free
(T₂,cycle)-free
(T₃,X₈₁,cycle)-free
(T₃,cycle)-free
Urquhart
V-perfect
VPG
W_2n+3-free
(W₄,W₅,butterfly)-free
(W₄,X₁₀₂,X₂₀₄,X₂₀₉,X₂₁₀,X₂₁₂,X₂₁₃,X₂₁₄,X₂₁₅,X₂₁₆,X₂₁₇,X₂₁₈,X₈₆,P₂ ∪ P₃,P₃ ∪ 2K₁,X₁₈₈,gem)-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
W_n+4-free
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
(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
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free
(X₄₂,T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,net)-free ∩ normal circular arc ∩ quasi-line
(X₇₉,X₈₀)-free
(X₇₉,X₈₀)-free ∩ modular
(X₉₁,claw)-free
(XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₇,XC₈)-free
XC₁₀-free
XC₁₀-free ∩ pseudo-modular
XC₁₀-free ∩ weakly modular
(XC₁₁,claw,diamond)-free
(XC₁₁,odd-cycle)-free
(XC₁₁,odd-cycle)-free ∩ planar
(XC₁₂,cycle)-free
(XC₁₂,triangle)-free
(XC₁₂,triangle)-free ∩ planar
XC₁₃-free
(XC₇,XC₁,XC₂,XC₃,XC₄,XC₅,XC₆,XC₈)-free
XC₉-free
(XF₁²ⁿ⁺³,XF₅²ⁿ⁺³,XF₆²ⁿ⁺²,C_n+6,T₂,X₂,X₃,X₃₀,X₃₁,X₃₂,X₃₃,X₃₄,X₃₅,X₃₆,co-XF₂ⁿ⁺¹,co-XF₃ⁿ,co-XF₄ⁿ,hole)-free
(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
β-perfect ∩ co-β-perfect
β-perfect ∩ perfect
(G)-perfect
₃-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
(3K₂,odd-hole,paw)-free
(5-pan,T₂,X₁₇₂)-free
(A,P₆,co-domino)-free
(A,T₂,odd anti-cycle)-free
BW₃-free
C₆-free
(C₇,odd-hole)-free
(C_n+3 ∪ K₁,co-diamond,co-paw)-free
(C_n+4,H)-free
(C_n+4,T₂,X₃₁,co-XF₂ⁿ⁺¹,co-XF₃ⁿ)-free
(C_n+4,T₂,co-XF₂ⁿ⁺¹)-free
(C_n+4,X₅₉,co-longhorn)-free
(C_n+4,bull,co-dart,co-gem)-free
(C_n+4,bull,house)-free
(C_n+4,co-claw,co-gem,house)-free
(C_n+4,co-claw,co-gem)-free
(C_n+4,co-claw)-free
(C_n+4,co-dart,co-gem)-free
(C_n+4,co-diamond)-free
(C_n+4,co-gem)-free
(C_n+4,co-sun)-free
(C_n+4,net)-free
(C_n+4,odd co-sun)-free
C_n+4-free
(C_n+6,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
C_n+6-free
C_n+7-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,triangle)-free
P₃-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
P₇-free
(T₂,X₂₀₅,X₂₀₆,X₂₀₇,X₂₀₈,even anti-hole,odd anti-cycle)-free
(T₂,co-cycle)-free
(T₃,X₈₁,co-cycle)-free
(T₃,co-cycle)-free
W_2n+3-free
(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
(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
(X₉₁,co-claw)-free
XC₁₀-free
(XC₁₁,co-claw,co-diamond)-free
(XC₁₁,odd anti-cycle)-free
XC₁₁-free
(XC₁₂,co-cycle)-free
XC₁₂-free
XC₁₃-free
(claw ∪ 3K₁,odd anti-cycle)-free
(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
absolute bipartite retract
absolute reflexive retract
absolutely perfect
absorbantly perfect
all-4-simplicial
almost CIS
almost claw-free
almost median
almost tree (1)
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
anti-hole-free
apex
astral triple-free
b-perfect
b-perfect ∩ chordal
balanced
balanced 2-interval
balanced ∩ chordal
balanced ∩ co-line
balanced ∩ line
balanced ∩ paw-free
bar visibility
basic 4-leaf power
basic perfect
bi-cograph
biclique separable
biclique-Helly
biconvex
bigeodetic
binary Hamming
binary tree
binary tree ∩ partial grid
bip^*
bipartable
bipartite
bipartite ∩ bithreshold
bipartite ∩ bounded tolerance
bipartite ∩ boxicity 2
bipartite ∩ bridged
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
biplanar
bipolarizable
bisplit
bisplit ∩ triangle-free
bithreshold
bitolerance
block
block duplicate
book thickness 2
bounded bitolerance
bounded cutwidth
bounded degree
bounded degree ∩ bounded treewidth
bounded multitolerance
bounded tolerance
bounded treewidth
boxicity 1
boxicity 2
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,fork)-free
(bull,hole,odd anti-hole)-free
(bull,house,odd-hole)-free
(bull,house)-free
(bull,odd anti-hole,odd-hole)-free
bull-free
bull-free ∩ perfect
bull-free ∩ strict quasi-parity
(butterfly,claw)-free
(butterfly,gem)-free
cactus
caterpillar
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-chordal ∩ co-comparability ∩ comparability
chordal ∩ co-comparability
chordal ∩ cograph
chordal ∩ comparability
chordal ∩ diametral path
chordal ∩ diamond-free
chordal ∩ distance-hereditary
chordal ∩ domination perfect
chordal ∩ domino
chordal ∩ dually chordal
chordal ∩ gem-free
chordal ∩ hamiltonian
chordal ∩ hamiltonian ∩ planar
chordal ∩ hereditary clique-Helly
chordal ∩ hereditary dominating pair
chordal ∩ irredundance perfect
chordal ∩ maximal planar
chordal ∩ neighbourhood perfect
chordal ∩ odd-sun-free
chordal ∩ planar
chordal ∩ probe diamond-free
chordal ∩ proper circular arc
chordal ∩ sun-free
chordal ∩ unipolar
chordal ∩ unit circular arc
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 ∩ co-bipartite
circular arc ∩ cograph
circular arc ∩ comparability
circular arc ∩ diamond-free
circular arc ∩ paw-free
circular arc ∩ perfect
circular convex bipartite
circular interval
circular perfect
circular permutation
circular strip
circular trapezoid
(claw ∪ 3K₁,odd-cycle)-free
(claw,co-claw)-free
(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-cycle)-free
(claw,odd-hole)-free
(claw,odd-hole)-free ∩ tripartite
(claw,paw)-free
claw-free
claw-free ∩ interval
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
clique graphs of Helly circular arc
clique graphs of interval
clique graphs of normal Helly circular arc
clique separable
clique-Helly
clique-Helly ∩ clique-chordal
clique-Helly ∩ dismantlable
clique-Helly ∩ dismantlable ∩ reflexive
clique-chordal
clique-perfect
clique-perfect ∩ triangle-free
cliquewidth 2
cliquewidth 3
cliquewidth 4
cluster
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-biconvex
co-bipartite
co-bipartite ∩ concave-round
co-bipartite ∩ normal circular arc
co-bipartite ∩ proper circular arc
co-bithreshold
co-bithreshold ∩ split
co-bounded tolerance
co-building-free
(co-butterfly,co-claw)-free
(co-butterfly,co-gem)-free
co-chordal
co-chordal ∩ comparability
co-chordal ∩ superperfect
co-circular perfect
(co-claw,co-cycle)-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,odd anti-hole)-free
(co-claw,odd-hole)-free
co-claw-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 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,even anti-cycle)-free
(co-diamond,house)-free
(co-diamond,odd anti-hole)-free
co-diamond-free
co-domino-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-gem-free
co-hereditary clique-Helly
co-interval
co-interval ∩ cograph
co-interval ∩ cograph ∩ interval
co-interval ∩ interval
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-paw-free
co-perfectly orderable
co-planar
co-probe cograph
co-probe threshold
co-proper interval bigraph
co-quasi-line
co-strongly chordal
co-sun-free
co-threshold tolerance
co-tolerance
co-trapezoid
co-trivially perfect
co-trivially perfect ∩ trivially perfect
co-unipolar
co-unipolar ∪ unipolar
co-unit interval
cograph
cograph ∩ interval
cograph ∩ split
cograph contraction
coin
comparability
comparability ∩ distance-hereditary
comparability ∩ split
comparability ∩ weakly chordal
comparability graphs of arborescence orders
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
comparability graphs of threshold orders
complete
complete Hamming
complete bipartite
complete multipartite
complete split
concave-round
containment graph of circles
containment graph of intervals
containment graphs
containment graphs of circular arcs
convex
convex-round
cop-win
(cross,triangle)-free
cubic
cubic ∩ hamiltonian
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
cubical
cycle-bicolorable
cycle-free
d-trapezoid
diametral path
(diamond,even-cycle)-free
(diamond,odd-hole)-free
diamond-free
diamond-free ∩ perfect
difference
directed path
disjoint union of stars
disk
disk contact
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
distance-hereditary
domination
domination perfect
domination perfect ∩ planar
domination perfect ∩ triangle-free
domino
(domino,gem,hole,house,net)-free
(domino,gem,house)-free
(domino,gem,house)-free ∩ pseudo-modular
(domino,hole,odd-cycle)-free
domino-free
domino-free ∩ modular
domishold
double split
doubled
doubly chordal
dually chordal
dually chordal ∩ tripartite
edge regular
equimatchable
even anti-cycle-free
even anti-hole-free
even-cycle-free
even-hole-free
even-hole-free ∩ probe chordal
even-signable
extended P₄-laden
extended P₄-reducible
extended P₄-sparse
forest-perfect
(fork,house)-free
(fork,odd-cycle)-free
(fork,triangle)-free
fork-free
frame hereditary dominating pair
fully cycle extendable
fuzzy circular interval
fuzzy linear interval
galled-tree explainable
galled-tree explainable ∩ house-free
gem-free
generalized split
generalized strongly chordal
generically minimally rigid
genus 0
genus 1
geodetic
girth >=9
good
graceful
grid
grid graph
grid graph ∩ maximum degree 3
grid intersection
gridline
half
half-disk Helly
hamiltonian
hamiltonian ∩ interval
hamiltonian ∩ planar
hamiltonian ∩ split
harmonious
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
hereditary clique-Helly ∩ line ∩ perfect
hereditary clique-Helly ∩ paw-free ∩ perfect
hereditary clique-Helly ∩ self-clique
hereditary disk-Helly
hereditary dismantlable
hereditary dominating pair
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
hereditary sat
hereditary weakly modular
(hole,odd anti-hole)-free
(hole,odd-cycle)-free
hole-free
hole-free ∩ planar
homogeneously orderable
homogeneously representable
homothetic triangle contact
(house,hole,domino,sun)-free
house-free
house-free ∩ weakly chordal
hypercube
i-triangulated
independent module-composed
indifference
indifference ∩ split
induced-hereditary pseudo-modular
intersection graph of nested intervals
intersection graphs of parallelograms (squares)
interval
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-DIR
k-SEG
k-outerplanar
k-path graph, fixed k
k-polygon
k-regular, fixed k
k-regular, fixed k>= 3
k-regular, fixed k>= 6
k-tree, fixed k
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 Helly hypergraphs of rank 3
line graphs of acyclic multigraphs
line graphs of bipartite graphs
line graphs of bipartite multigraphs
line graphs of linear Helly hypergraphs of rank 3
line graphs of multigraphs without triangles
line graphs of planar cubic bipartite graphs
line graphs of triangle-free graphs
line perfect
linear NLC-width 1
linear arboricity <= 2
linear cliquewidth 2
linear domino
linear domino ∩ maximum degree 4
linear forest
linear interval
linearly convex triangular grid graph
lobster
locally bipartite
locally chordal
locally connected
locally connected ∩ maximum degree 4
locally connected ∩ maximum degree 7
locally connected ∩ triangular grid graph
locally perfect
locally split
map
matrogenic
matroidal
max-tolerance
maxibrittle
maximal clique irreducible
maximal outerplanar
maximal planar
maximum degree 1
maximum degree 3
maximum degree 3 ∩ planar ∩ triangle-free
maximum degree 4
maximum degree 5
maximum degree 6
maximum degree 7
median
median ∩ planar
middle
min leaf power
minimally imperfect
mock threshold
mock threshold ∩ split
modular
modular ∩ open-neighbourhood-Helly
module-composed
monopolar
multitolerance
murky
(n+4)-pan-free
nK₂-free, fixed n
nP₃-free, fixed n
nearly bipartite
neighbourhood chordal
neighbourhood perfect
neighbourhood-Helly
neighbourhood-Helly ∩ pseudo-modular ∩ reflexive
neighbourhood-Helly ∩ triangle-free
net-free
normal
normal Helly circular arc
normal circular arc
odd anti-cycle-free
(odd anti-hole,odd-hole)-free
odd anti-hole-free
(odd building,odd-hole)-free
odd co-sun-free
odd-cycle ∪ K₁-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
odd-hole-free ∩ planar
odd-hole-free ∩ pretty
odd-signable
odd-signable ∩ triangle-free
odd-sun-free
open-neighbourhood-Helly
opposition
outer-string
outerplanar
overlap
(p,q)-colorable
(p,q)-split
(p,q<=2)-colorable
p-connected
p-tree
pairwise compatibility
parallelepiped
parity
partial 2-tree
partial 3-tree
partial 3-tree ∩ planar
partial 3d grid
partial 4-tree
partial bar visibility
partial cube
partial grid
partial k-tree, fixed k
partial rectangle visibility
partitionable
partner-limited
path orderable
paw-free
paw-free ∩ perfect
penny
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
perfect cochromatic
perfect connected-dominant
perfect elimination bipartite
perfectly 1-transversable
perfectly colorable
perfectly contractile
perfectly orderable
permutation
permutation ∩ split
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polar
polyhedral
power-chordal
premedian
preperfect
pretty
probe (1,2)-colorable
probe (2,2)-colorable
probe AT-free
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-bipartite
probe co-comparability
probe co-trivially perfect
probe co-trivially perfect ∩ probe trivially perfect
probe cograph
probe comparability
probe complete
probe diamond-free
probe distance-hereditary
probe interval
probe interval ∩ tree
probe interval bigraph
probe permutation
probe proper interval
probe ptolemaic
probe split
probe strongly chordal
probe threshold
probe threshold ∩ split
probe trivially perfect
probe unit interval
proper Helly circular arc
proper chordal
proper circular arc
proper interval
proper interval bigraph
proper tolerance
pseudo-median
pseudo-median ∩ triangle-free
pseudo-modular
pseudo-modular ∩ triangle-free
pseudo-split
ptolemaic
ptolemaic ∩ weakly geodetic
(q, q-3), fixed q>= 7
(q,q-4), fixed q
(q,t)
quasi-Meyniel
quasi-brittle
quasi-line
quasi-median
quasi-parity
quasi-threshold
quasitriangulated
rectagraph
rectangle intersection
rectangle visibility
reflexive
relative neighbourhood graph
restricted block duplicate
rigid circuit
rooted directed path
self-clique
self-complementary
semi-P₄-sparse
semi-median
semi-square intersection
semicircular
semiperfectly orderable
series-parallel
short-chorded
skeletal
slender
slightly triangulated
slim
solid grid graph
solid triangular grid graph
spider graph
split
split ∩ strongly chordal
split ∩ superperfect
split ∩ threshold signed
split-neighbourhood
split-perfect
square of tree
star convex
starlike
starlike threshold
strict 2-threshold
strict B₁-VCPG
strict quasi-parity
strictly chordal
strictly clique irreducible
string
strong asteroid free
strong domination perfect
strong tree-cograph
strongly 3-colorable
strongly brittle
strongly chordal
strongly circular perfect
strongly even-signable
strongly odd-signable
strongly orderable
strongly perfect
strongly regular
subhamiltonian
substar
subtree filament
subtree overlap
sun-free
sun-free ∩ weakly chordal
superbrittle
superfragile
superperfect
thick tree
thickness <= 2
threshold
threshold signed
threshold tolerance
tolerance
tolerance ∩ tree
tolerance ∩ triangle-free
toroidal
totally unimodular
trapezoepiped
trapezoid
tree
tree convex
tree-cograph
tree-perfect
treewidth 2
treewidth 3
treewidth 4
treewidth 5
triad convex
triangle contact
triangle-free
triangular grid graph
triangulated
tripartite
trivially perfect
unbreakable
undirected path
unicyclic
unigraph
unimodular
unipolar
unit 2-circular arc
unit 2-circular track
unit 2-interval
unit 2-track
unit 3-circular track
unit 3-interval
unit 3-track
unit Helly circle
unit Helly circular arc
unit bar visibility
unit circular arc
unit disk
unit grid intersection
unit interval
unit interval bigraph
unit square
unit tolerance
universally signable
upper domination perfect
upper irredundance perfect
very strongly perfect
visibility
walk regular
weak bar visibility
weak bipolarizable
weak bisplit
weak dominating pair
weak rectangle visibility
weakly bridged
weakly chordal
weakly geodetic
weakly median
weakly modular
well covered
well-dominated
well-partitioned chordal
wing-triangulated