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Filtering is case insensitive and the filtering process has some limited knowledge about graph names. E.g. if you filter on 'chair', 'fork' will also be found. Use LaTeX notation for super-/subscripts e.g. K_3 for K3 or S_{1,1,2} for S1,1,2 and for intersection/union (cap/cup).

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 (0,2)-colorable 
 (0,2)-colorable cap chordal 
 (0,3)-colorable 
 (0,3)-colorable cap chordal 
 (1,1)-colorable 
 (1,2)-colorable 
 (1,2)-colorable cap chordal 
 (1,2)-polar 
 (1,2)-polar cap chordal 
 1-bounded bipartite 
 1-bounded tripartite 
 (2,0)-colorable 
 (2,0)-colorable cap chordal 
 (2,2)-colorable 
 (2,2)-colorable cap chordal 
 2-bounded bipartite 
 2-connected 
 2-connected cap (4-fan,Cn+4,K5 - e,S3,co-(H),co-(K3 cup 2K1))-free 
 2-interval 
 2-leaf power 
 2-outerplanar 
 2-split 
 2-split cap perfect 
 2-subdivision 
 2-subdivision cap planar 
 2-threshold 
 2-tree 
 2-tree cap probe interval 
 (2C4,3K2,C6,E,P2 cup P4,P6,X25,X26,X27,X28,X29,odd-cycle)-free 
 (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(K1,4),co-(X85))-free 
 (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(X85))-free 
 (2K2,4K1,co-claw,co-diamond)-free 
 (2K2,A,H)-free 
 (2K2,C4,C5,H,S3,X160,co-(X159),net,rising sun)-free 
 (2K2,C4,C5,S3,X159,X160,co-(H),co-rising sun,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,co-sun)-free 
 (2K2,C4,C5,sun)-free 
 (2K2,C4,C5)-free 
 (2K2,C4,P4)-free 
 (2K2,C4)-free 
 (2K2,C5,S3,X159,X160,X161,X162,X46,X70,co-(2P3),co-(3K2),co-(H),co-(P2 cup P4),co-(X1),co-rising sun,house,net)-free 
 (2K2,C5,co-(C6),co-(C7),co-(C8),co-claw,co-diamond)-free 
 (2K2,C5,co-(T2))-free 
 (2K2,C5,triangle)-free 
 (2K2,C5)-free 
 (2K2,K3,3,K3,3+e,P4,co-(2P3))-free 
 (2K2,P4,co-dart)-free 
 (2K2,P4)-free 
 (2K2,co-(C6),odd anti-cycle)-free 
 (2K2,co-(P6))-free 
 (2K2,co-(X91),co-claw)-free 
 (2K2,claw)-free 
 (2K2,co-diamond)-free 
 (2K2,house)-free 
 (2K2,odd-cycle)-free 
 2K2-free 
 2K2-free cap bipartite 
 2K2-free cap probe cograph 
 2K2-free cap probe trivially perfect 
 (2K3 + e,3K1,C5,co-(T2),co-(X18),co-(X94),co-domino)-free 
 (2K3 + e,C5,C6,P6,X5,co-(2P4),co-(A),co-(C6),co-(C7),co-(E),co-(P7),co-(R),co-(X1),co-(X103),co-(X5),co-(X58),co-(X84),co-(X98),antenna,co-domino,co-rising sun,co-twin-house,domino,parachute,parapluie,rising sun,sunlet4)-free 
 (2K3 + e,co-(X98),house)-free 
 (2K3 + e,co-(X99),house)-free 
 (2K3 + e,house)-free 
 (2K3,2K3 + e,3K1,co-(A),co-(H),co-(T2),co-(X18),co-(X45),co-domino)-free 
 (2K3,2K3 + e,co-(A),co-(H),co-(X45),co-(XZ5),co-domino)-free 
 (2K3,2P3,C4,K3 cup P3,P4)-free 
 (2K3,2P3,C5,C6,C7,K2,3,K3 cup P3,X84,co-(3K2),co-(C4 cup P2),co-(C6),co-(P2 cup P4),co-(P6),co-(X18),co-(X5),co-antenna,co-domino,co-fish)-free 
 (2K3,2P3,Cn+4,K3 cup P3)-free 
 (2K3,3K1,co-(A),co-(H),co-(X45))-free 
 (2K3,4K1,C7,X38,X39,co-(W4 cup K1),co-(W5),co-(X86),co-(X87),co-(X88),co-(X89),co-(X90),butterfly cup K1,diamond)-free 
 (2K3,Cn+4)-free 
 (2K3,X42,co-(A),co-(H),co-(X45),co-(X46),co-(X47),co-(X48),co-(X49),co-(X50),co-(X51),co-(X52),co-(X53),co-(X54),co-(X55),co-(X56),co-(X57))-free 
 (2K3,house)-free 
 (2K4,house)-free 
 (2P3,3K2,C4 cup P2,C6,K2,3,P6,X130,X132,X134,X152,X153,X154,X155,X156,X157,X158,X18,X84,co-(X11),co-(X127),co-(X128),co-(X129),co-(X131),co-(X133),co-(X135),co-(X136),co-(X137),co-(X138),co-(X139),co-(X140),co-(X141),co-(X142),co-(X143),co-(X144),co-(X145),co-(X146),co-(X147),co-(X148),co-(X149),co-(X150),co-(X151),co-(X30),co-(X35),co-(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 cup P4,P5,S3,X1,X160,co-(X159),co-(X161),co-(X162),co-(X46),co-(X70),net,rising sun)-free 
 (2P4,A,C5,C6,C7,E,K3,3-e,P7,R,X1,X103,X5,X58,X84,X98,co-(C6),co-(P6),co-(X5),co-(sunlet4),co-antenna,co-domino,co-rising sun,domino,parachute,parapluie,rising sun,twin-house)-free 
 3-Helly 
 3-interval 
 3-leaf power 
 3-mino 
 (3K1,C4,C5)-free 
 (3K1,C5,K3 cup K4,co-(BW3),co-(K3,4-e),co-(T2),co-(X18),co-(X92),co-(X93))-free 
 (3K1,C5,K5 - e,co-(C6 cup K1),co-(C7),co-(K3,3 cup K1),co-(K3,3-e cup K1),co-(domino cup K1))-free 
 (3K1,C5,butterfly,diamond)-free 
 (3K1,co-(E))-free 
 (3K1,co-(H))-free 
 (3K1,co-(T2),co-(X2),co-(X3),anti-hole)-free 
 (3K1,co-cross)-free 
 (3K1,co-fork)-free 
 (3K1,house)-free 
 (3K2,C4 cup P2,C5,C6,K2 cup K3,K3,3,K3,3+e,P2 cup P4,P6,X18,X5,co-(2P3),co-(C6),co-(C7),co-(X84),antenna,domino,fish)-free 
 (3K2,C4 cup P2,C5,P2 cup P4,P5,S3,X1,X46,X70,co-(3K2),co-(C4 cup P2),co-(P2 cup P4),co-(X1),co-(X46),co-(X70),co-fish,co-rising sun,fish,house,net,rising sun)-free 
 (3K2,E,P2 cup P4,net)-free 
 (3K2,co-(P),co-gem,house)-free 
 (3K3,Cn+4)-free 
 (4-fan,Cn+4,K5 - e,S3,X100,X101,X102,co-(H),co-(K3 cup 2K1))-free 
 (4-fan,Cn+4,K5 - e,S3,co-(H),co-(K3 cup 2K1))-free 
 (4-fan,K1,4,W4,W5,co-(A cup K1),co-(co-fork cup K1),co-(gem cup K1),co-(net cup K1))-free 
 4-leaf power 
 (4K1,K4)-free 
 (4K1,P4)-free 
 (4K1,co-(Cn+4))-free 
 (4K1,house)-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 
 (6,1)-chordal 
 (6,1)-chordal cap bipartite 
 (6,1)-even-chordal 
 (6,2) 
 (6,2)-chordal 
 (6,2)-chordal cap bipartite 
 (6,3) 
 (7,3) 
 (7,4) 
 (7,5) 
 (8,4) 
 (9,6) 
 (A cup K1,co-(K1,4),co-(W4),co-(W5),co-4-fan,co-fork cup K1,gem cup K1,net cup K1)-free 
 (A,C4 cup 2K1,P2 cup P3,R,co-(K5 - e),co-(W5),co-claw,twin-C5,twin-house)-free 
 (A,C4 cup 2K1,P2 cup P3,R,co-(K5 - e),co-claw,odd anti-hole,twin-house)-free 
 (A,C5,P5,co-(A),house,parachute,parapluie)-free 
 (A,E,S3,X1,domino,hole,house,net,rising sun)-free 
 (A,H,K3,3,K3,3-e,T2,X18,X45,domino,triangle)-free 
 (A,H,K3,3,K3,3-e,X45,XZ5,domino)-free 
 (A,H,K3,3,X45,X46,X47,X48,X49,X50,X51,X52,X53,X54,X55,X56,X57,co-(X42))-free 
 (A,H,K3,3,X45,triangle)-free 
 (A,P6,clique wheel,domino,hole,house)-free 
 (A,P6,domino)-free 
 (A,T2,odd-cycle)-free 
 AC 
 AT-free 
 AT-free cap bipartite 
 AT-free cap chordal 
 AT-free cap claw-free 
 (BW3,C5,K3,4,K3,4-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,co-(C6),co-(C8),co-(T2),co-(X3))-free 
 BW3-free 
 BW3-free cap modular 
 Berge 
 Berge cap bull-free 
 Berge cap claw-free 
 Birkhoff 
 Bouchet 
 (C4,C5,C6,C7,C8,H,K1,4,X85,triangle)-free 
 (C4,C5,C6,C7,C8,H,X85,triangle)-free 
 (C4,C5,C6,C7,C8,H,X85,triangle)-free cap K1,4-free 
 (C4,C5,C6,C7,C8,claw,diamond)-free 
 (C4,C5,T2)-free 
 (C4,C5)-free 
 (C4,C5)-free cap Helly 
 (C4,C5)-free cap cop-win 
 (C4,C6,odd-cycle)-free 
 (C4,K4,claw,diamond)-free 
 (C4,P4,dart)-free 
 (C4,P4)-free 
 (C4,P5)-free 
 (C4,P6)-free 
 (C4,X91,claw)-free 
 (C4,co-(A),co-(H))-free 
 (C4,co-claw)-free 
 (C4,diamond)-free 
 (C4,odd anti-cycle)-free 
 C4-free 
 C4-free cap C6-free cap bipartite 
 C4-free cap co-comparability 
 C4-free cap induced-hereditary pseudo-modular 
 (C5,C6 cup K1,C7,K3,3 cup K1,K3,3-e cup K1,co-(K5 - e),domino cup K1,triangle)-free 
 (C5,C6,C7,C8,P8,X19,X20,X21,X22,gem,house)-free 
 (C5,C6,P6,X17,X18,X5,X98,co-(C6),co-(P6),antenna,domino)-free 
 (C5,C6,P6,co-(C6),co-(P6),co-(X17),co-(X18),co-(X5),co-(X98),co-antenna,co-domino)-free 
 (C5,C6,P6,co-(C6),co-(P6))-free 
 (C5,K2 cup K3,K2,3,P,P2 cup P3,P5,co-(P),co-(P2 cup P3),co-fork,fork,house)-free 
 (C5,K3,3-e,T2,X18,X94,domino,triangle)-free 
 (C5,P,P5,S3,co-(P),co-fork,fork,house,net)-free 
 (C5,P,P5,co-(P),bull,co-gem,fork)-free 
 (C5,P,P5,co-(P),co-fork,fork,house)-free 
 (C5,P,P5,co-(P),house)-free 
 (C5,P,P5,house)-free 
 (C5,P,co-(P),bull,co-fork,gem,house)-free 
 (C5,P,co-fork,fork,gem,house)-free 
 (C5,P2 cup P3,house)-free 
 (C5,P5,co-(C6),co-(C7),co-(C8),co-(P8),co-(X19),co-(X20),co-(X21),co-(X22),co-gem)-free 
 (C5,P5,co-(P),co-fork,co-gem,fork)-free 
 (C5,P5,co-(P),house)-free 
 (C5,P5,co-(P2 cup P3))-free 
 (C5,P5,co-fish,fish,house)-free 
 (C5,P5,gem)-free 
 (C5,P5,house)-free 
 (C5,P5)-free 
 (C5,P6,co-(P6))-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 cap P4-extendible 
 C5-free cap P4-tidy 
 C5-free cap matrogenic 
 (C6,C8,T2,X3,co-(BW3),co-(W5),co-(W7),co-(X103),co-(X105),co-(X106),co-(X107),co-(X108),co-(X109),co-(X110),co-(X111),co-(X112),co-(X113),co-(X114),co-(X115),co-(X116),co-(X117),co-(X118),co-(X119),co-(X120),co-(X121),co-(X122),co-(X123),co-(X124),co-(X125),co-(X126),co-(X53),co-(X88),co-X104)-free 
 (C6,K3,3+e,P,P7,X37,X41)-free 
 (C6,P6,co-(P6),co-(X10),co-(X11),co-(X12),co-(X13),co-(X14),co-(X15),co-(X5),co-(X6),co-(X7),co-(X8),co-(X9),anti-hole,co-antenna)-free 
 (C6,co-(C6))-free 
 (C6,co-(C6))-free murky 
 (C6,house)-free 
 C6-free 
 C6-free cap modular 
 (Cn+4,H)-free 
 (Cn+4,K4)-free 
 (Cn+4,P5,bull)-free 
 (Cn+4,P5,claw,gem)-free 
 (Cn+4,S3 cup K1,claw,net)-free 
 (Cn+4,S3,claw,net)-free 
 (Cn+4,S3,net)-free 
 (Cn+4,S3)-free 
 (Cn+4,T2,X31,XF2n+1,XF3n)-free 
 (Cn+4,T2,XF2n+1)-free 
 (Cn+4,T2,net)-free 
 (Cn+4,X59,longhorn)-free 
 (Cn+4,XF12n+3,XF62n+2,co-(X34),co-(X36),co-XF2n+1,co-XF3n)-free 
 (Cn+4,XF2n+1,XF3n,claw)-free 
 (Cn+4,bull,dart,gem)-free 
 (Cn+4,claw,gem)-free 
 (Cn+4,claw,net)-free 
 (Cn+4,claw)-free 
 (Cn+4,diamond)-free 
 (Cn+4,gem)-free 
 (Cn+4,odd-sun)-free 
 (Cn+4,sun)-free 
 Cn+4-free 
 (Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39,X40,X41,XF2n+1,XF3n,XF4n)-free 
 (Cn+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 
 (Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X36,XF12n+3,XF2n+1,XF3n,XF4n,XF52n+3,XF62n+2,co-(Cn+6),co-(T2),co-(X2),co-(X3),co-(X30),co-(X31),co-(X32),co-(X33),co-(X34),co-(X36),co-XF12n+3,co-XF2n+1,co-XF3n,co-XF4n,co-XF52n+3,co-XF62n+2,odd anti-hole)-free 
 (Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X36,XF12n+3,XF2n+1,XF3n,XF4n,XF52n+3,XF62n+2,co-(Cn+6),co-(T2),co-(X2),co-(X3),co-(X30),co-(X31),co-(X32),co-(X33),co-(X34),co-(X36),co-XF12n+3,co-XF2n+1,co-XF3n,co-XF4n,co-XF52n+3,co-XF62n+2,odd-hole)-free 
 (Cn+6,X37,claw,co-antenna,net,sun)-free 
 D 
 Dilworth 1 
 Dilworth 2 
 Dilworth 3 
 Dilworth 4 
 (E,P)-free 
 (E,odd-cycle)-free 
 (E,triangle)-free 
 E-free 
 E-free cap bipartite 
 EPT 
 EPT cap chordal 
 Fn grid 
 Gallai 
 Gallai-perfect 
 (H,K3 cup 2K1,co-(Cn+4),co-(K5 - e),co-(X100),co-(X101),co-(X102),co-4-fan,net)-free 
 (H,K3 cup 2K1,co-(Cn+4),co-(K5 - e),co-4-fan,net)-free 
 (H,triangle)-free 
 HH-free 
 HHD-free 
 HHD-free cap co-HHD-free 
 HHDA-free 
 HHDG-free 
 HHDS-free 
 HHDbicycle-free 
 HHG-free 
 HHP-free 
 Halin 
 Hamiltonian hereditary 
 Helly 
 Helly cap bridged 
 Helly cap reflexive 
 Helly chordal 
 Helly chordal cap clique-chordal 
 Helly circular arc 
 Hilbertian 
 Hn,q grid 
 (K1,4,P,P5,fork)-free 
 (K1,4,P5)-free 
 (K1,4,diamond)-free 
 K1,4-free 
 (K2 cup K3,P5,co-(X37),co-(X38),co-diamond,co-domino,co-twin-C5)-free 
 (K2 cup 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,co-(2P3),co-(3K2),co-(C4 cup P2),co-(C6),co-(P6),co-(X130),co-(X132),co-(X134),co-(X152),co-(X153),co-(X154),co-(X155),co-(X156),co-(X157),co-(X158),co-(X18),co-(X84),antenna,co-domino,co-fish,eiffeltower,longhorn,odd-hole)-free 
 (K2 cup K3,co-(P),co-(X163),co-(X95),co-diamond,house)-free 
 (K2 cup K3,co-(P),anti-hole)-free 
 (K2 cup K3,co-(P),house)-free 
 (K2 cup K3,co-diamond)-free 
 (K2 cup K3,house)-free 
 K2 cup K3-free 
 K2 cup claw-free 
 (K2,3,P,P5,X163,X95,diamond)-free 
 (K2,3,P,P5)-free 
 (K2,3,P,hole)-free 
 (K2,3,P5)-free 
 (K2,3,X37,X38,diamond,domino,house,twin-C5)-free 
 (K2,3,diamond)-free 
 (K2,3,diamond)-free cap weakly modular 
 K2,3-free 
 K2,3-free cap hereditary modular 
 (K3 cup P3,co-(C6),co-(P),co-(P7),co-(X37),co-(X41))-free 
 (K3,3,3,co-(Cn+4))-free 
 (K3,3,K3,3+e,co-(2P3),co-(Cn+4))-free 
 (K3,3,K4,W4 cup K1,W5,X86,X87,X88,X89,X90,co-(C7),co-(X38),co-(X39),co-(butterfly cup K1),co-diamond)-free 
 (K3,3,P5)-free 
 (K3,3,co-(Cn+4))-free 
 (K3,3-e,P5,X98)-free 
 (K3,3-e,P5,X99)-free 
 (K3,3-e,P5)-free 
 (K4,4,P5)-free 
 (K4,P4)-free 
 (K4,P5)-free 
 (K4,odd anti-hole,odd-hole)-free 
 K4-free 
 K4-free cap perfect 
 K4-minor-free 
 (K5 - e,W5,co-(A),co-(C4 cup 2K1),co-(P2 cup P3),co-(R),claw,co-twin-C5,co-twin-house)-free 
 (K5 - e,co-(A),co-(C4 cup 2K1),co-(P2 cup P3),co-(R),claw,co-twin-house,odd-hole)-free 
 Matula perfect 
 Meyniel 
 Meyniel cap co-Meyniel 
 N* 
 N*-perfect 
 (P,P5,S3,co-(P),co-fork,fork,house,net)-free 
 (P,P5,co-(3K2),gem)-free 
 (P,P5,co-(P),co-fork,fork,house)-free 
 (P,P5,co-fork)-free 
 (P,P5)-free 
 (P,P7)-free 
 (P,P8)-free 
 (P,T2)-free 
 (P,co-(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,star1,2,3)-free 
 (P,star1,2,4)-free 
 (P,star1,2,5)-free 
 P-free 
 (P2 cup P3,house)-free 
 P3-free 
 P4-bipartite 
 P4-brittle 
 P4-comparability 
 P4-extendible 
 P4-extendible cap P4-sparse 
 P4-free 
 P4-indifference 
 P4-laden 
 P4-lite 
 P4-reducible 
 P4-simplicial 
 P4-sparse 
 P4-tidy 
 (P5,S3,co-(A),co-(E),co-(X1),anti-hole,co-domino,co-rising sun,net)-free 
 (P5,X82,X83)-free 
 (P5,co-(A),co-(P6),anti clique wheel,anti-hole,co-domino)-free 
 (P5,co-(A),anti-hole,co-domino)-free 
 (P5,co-(C6))-free 
 (P5,co-(C6))-free cap weakly chordal 
 (P5,co-(P),anti-hole)-free 
 (P5,co-(P),gem)-free 
 (P5,co-(P2 cup P3))-free 
 (P5,co-(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 cap 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 cap tripartite 
 (P6,X10,X11,X12,X13,X14,X15,X5,X6,X7,X8,X9,co-(C6),co-(P6),antenna,hole)-free 
 (P6,X30,X8)-free 
 P6-free 
 P6-free cap tripartite 
 (P7,odd-cycle,star1,2,3,sunlet4)-free 
 (P7,odd-cycle,star1,2,3)-free 
 P7-free 
 PI 
 PI* 
 Raspail 
 (S3,S4,net)-free 
 (S3,co-(3K2),co-(E),co-(P2 cup P4))-free 
 (S3,co-(Cn+4),co-(S3 cup K1),co-claw)-free 
 (S3,co-(Cn+4),co-(T2))-free 
 (S3,co-(Cn+4),co-claw,net)-free 
 (S3,co-(Cn+4),co-claw)-free 
 (S3,co-(Cn+4),net)-free 
 (S3,co-(Cn+6),co-(X37),antenna,co-claw,co-sun)-free 
 (S3,claw,net)-free 
 (S3,claw,net)-free cap chordal 
 (S3,co-claw,net)-free 
 (S3,co-claw)-free 
 (S3,net)-free 
 (S3,net)-free cap chordal 
 (S3,net)-free cap extended P4-sparse 
 (S3,net)-free cap split 
 (S3,net)-free cap sun-free 
 S3-free 
 S3-free cap chordal 
 (T2,X2,X3,X30,X31,X32,X33,X34,X35,X36,XF2n+1,XF3n,XF4n,anti-hole,co-XF12n+3,co-XF52n+3,co-XF62n+2,hole)-free 
 (T2,X2,X3,hole,triangle)-free 
 (T2,cycle)-free 
 (T3,X81,cycle)-free 
 V-perfect 
 (W4,W5,butterfly)-free 
 (W4,claw,gem,odd-hole)-free 
 (W4,claw,gem)-free 
 (W4,claw)-free 
 (W4,gem)-free 
 (W4,gem)-free cap short-chorded 
 Welsh-Powell opposition 
 Welsh-Powell perfect 
 X-chordal 
 X-chordal cap X-conformal cap bipartite 
 X-chordal cap bipartite 
 X-conformal 
 X-conformal cap bipartite 
 X-conformal cap bipartite cap hereditary X-chordal 
 X-star-chordal 
 (X12,X5,X95,X96,X97,co-(X12),co-(X5),co-(X95),co-(X96),co-(X97),co-(claw cup triangle),claw cup triangle,co-cricket,co-twin-house,cricket,odd anti-hole,odd-hole,twin-house)-free 
 (X30,XZ1,XZ4,longhorn)-free 
 (X34,X36,XF2n+1,XF3n,co-(Cn+4),co-XF12n+3,co-XF62n+2)-free 
 (X38,gem,house)-free 
 (X79,X80)-free 
 (X79,X80)-free cap modular 
 (XC1,XC2,XC3,XC4,XC5,XC6,XC7,XC8)-free 
 XC10-free 
 XC10-free cap pseudo-modular 
 (XC11,claw,diamond)-free 
 (XC11,claw,diamond)-free cap tripartite 
 XC11-free 
 XC11-free cap linear domino cap tripartite 
 XC12-free 
 (XC7,co-(XC1),co-(XC2),co-(XC3),co-(XC4),co-(XC5),co-(XC6),co-(XC8))-free 
 XC9-free 
 (XF12n+3,XF52n+3,XF62n+2,co-(Cn+6),co-(T2),co-(X2),co-(X3),co-(X30),co-(X31),co-(X32),co-(X33),co-(X34),co-(X35),co-(X36),co-XF2n+1,co-XF3n,co-XF4n,odd-hole)-free 
 (XF12n+3,XF52n+3,XF62n+2,co-(T2),co-(X2),co-(X3),co-(X30),co-(X31),co-(X32),co-(X33),co-(X34),co-(X35),co-(X36),anti-hole,co-XF2n+1,co-XF3n,co-XF4n,hole)-free 
 cal C(G)-perfect 
 cal P3-perfect 
 (co-(2C4),co-(3K2),co-(C6),co-(E),co-(P2 cup P4),co-(P6),co-(X25),co-(X26),co-(X27),co-(X28),co-(X29),odd anti-cycle)-free 
 (co-(A),co-(P6),co-domino)-free 
 (co-(A),co-(T2),odd anti-cycle)-free 
 co-(BW3)-free 
 (co-(Cn+4),co-(H))-free 
 (co-(Cn+4),co-(T2),co-(X31),co-XF2n+1,co-XF3n)-free 
 (co-(Cn+4),co-(T2),co-XF2n+1)-free 
 (co-(Cn+4),co-(X59),co-longhorn)-free 
 (co-(Cn+4),bull,co-dart,co-gem)-free 
 (co-(Cn+4),bull,house)-free 
 (co-(Cn+4),co-XF2n+1,co-XF3n,co-claw)-free 
 (co-(Cn+4),co-claw,co-gem,house)-free 
 (co-(Cn+4),co-claw,co-gem)-free 
 (co-(Cn+4),co-claw)-free 
 (co-(Cn+4),co-diamond)-free 
 (co-(Cn+4),co-gem)-free 
 (co-(Cn+4),co-sun)-free 
 (co-(Cn+4),net)-free 
 (co-(Cn+4),odd co-sun)-free 
 co-(Cn+4)-free 
 (co-(Cn+6),co-(T2),co-(X2),co-(X3),co-(X30),co-(X31),co-(X32),co-(X33),co-(X34),co-(X35),co-(X36),co-(X37),co-(X38),co-(X39),co-(X40),co-(X41),co-XF2n+1,co-XF3n,co-XF4n)-free 
 (co-(E),co-(P))-free 
 (co-(E),odd anti-cycle)-free 
 (co-(K1,4),co-(P),co-fork,house)-free 
 (co-(K1,4),co-diamond)-free 
 (co-(K1,4),house)-free 
 co-(K1,4)-free 
 co-(K2 cup claw)-free 
 (co-(P),co-(P7))-free 
 (co-(P),co-(P8))-free 
 (co-(P),co-(T2))-free 
 (co-(P),co-(star1,2,3))-free 
 (co-(P),butterfly,fork,gem)-free 
 (co-(P),co-star1,2,4)-free 
 (co-(P),co-star1,2,5)-free 
 (co-(P),fork,gem)-free 
 (co-(P),fork,house)-free 
 (co-(P),fork)-free 
 (co-(P),house)-free 
 co-(P3)-free 
 (co-(P6),co-(X30),co-(X8))-free 
 (co-(P7),co-(star1,2,3),co-(sunlet4),odd anti-cycle)-free 
 (co-(P7),co-(star1,2,3),odd anti-cycle)-free 
 (co-(T2),co-cycle)-free 
 (co-(T3),co-(X81),co-cycle)-free 
 (co-(W4),co-(W5),co-butterfly)-free 
 (co-(W4),co-claw,co-gem,odd anti-hole)-free 
 (co-(W4),co-claw,co-gem)-free 
 (co-(W4),co-claw)-free 
 (co-(W4),co-gem)-free 
 (co-(X30),co-(XZ1),co-(XZ4),co-longhorn)-free 
 (co-(X79),co-(X80))-free 
 (co-(X82),co-(X83),house)-free 
 co-(XC10)-free 
 (co-(XC11),co-claw,co-diamond)-free 
 co-(XC11)-free 
 co-(XC12)-free 
 (co-(star1,2,3),co-(sunlet4),odd anti-cycle)-free 
 (co-(star1,2,3),odd anti-cycle)-free 
 tauk-perfect for all k >= 2 
 absolute bipartite retract 
 absolute reflexive retract 
 absolutely perfect 
 absorbantly perfect 
 almost tree (1) 
 alternately colourable 
 alternately orientable 
 alternately orientable cap co-comparability 
 (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 
 astral triple-free 
 bar visibility 
 basic 4-leaf power 
 bi-cograph 
 biclique separable 
 biconvex 
 bigeodetic 
 bip* 
 bipartable 
 bipartite 
 bipartite cap bithreshold 
 bipartite cap boxicity 2 
 bipartite cap bridged 
 bipartite cap claw-free 
 bipartite cap co-perfectly orderable 
 bipartite cap co-trapezoid 
 bipartite cap convex-round 
 bipartite cap distance-hereditary 
 bipartite cap grid intersection 
 bipartite cap probe interval 
 bipartite cap weakly chordal 
 bipartite cup co-bipartite cup co-line graphs of bipartite graphs cup line graphs of bipartite graphs 
 bipartite chain 
 bipartite permutation 
 bipartite tolerance 
 biplanar 
 bipolarizable 
 bisplit 
 bisplit cap triangle-free 
 bithreshold 
 block 
 bounded multitolerance 
 bounded tolerance 
 bounded treewidth 
 boxicity 1 
 boxicity 2 
 bridged 
 bridged cap clique-Helly 
 brittle 
 (bull,co-fork,co-gem)-free 
 (bull,co-fork,fork)-free 
 (bull,co-fork)-free 
 (bull,co-gem,gem)-free 
 (bull,fork,gem)-free 
 (bull,fork,house)-free 
 (bull,fork)-free 
 (bull,house,odd-hole)-free 
 (bull,house)-free 
 (bull,odd anti-hole,odd-hole)-free 
 bull-free 
 bull-free cap perfect 
 cactus 
 caterpillar 
 caterpillar arboricity <= 2 
 charming 
 chordal 
 chordal cap (claw,net)-free 
 chordal cap claw-free 
 chordal cap clique-Helly 
 chordal cap clique-chordal 
 chordal cap co-chordal 
 chordal cap co-chordal cap co-comparability cap comparability 
 chordal cap co-comparability 
 chordal cap cograph 
 chordal cap comparability 
 chordal cap diametral path 
 chordal cap diamond-free 
 chordal cap distance-hereditary 
 chordal cap dominating pair 
 chordal cap domination perfect 
 chordal cap domino 
 chordal cap dually chordal 
 chordal cap gem-free 
 chordal cap hereditary clique-Helly 
 chordal cap irredundance perfect 
 chordal cap neighbourhood perfect 
 chordal cap odd-sun-free 
 chordal cap proper circular arc 
 chordal cap sun-free 
 chordal cap unit circular arc 
 chordal cup co-chordal 
 chordal bipartite 
 chordal-perfect 
 circle 
 circle graph with equator 
 circle-polygon 
 circular arc 
 circular arc cap co-bipartite 
 circular arc cap comparability 
 circular convex bipartite 
 circular perfect 
 circular permutation 
 (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 cap tripartite 
 (claw,odd-cycle)-free 
 (claw,odd-hole)-free 
 (claw,odd-hole)-free cap tripartite 
 (claw,paw)-free 
 claw-free 
 claw-free cap interval 
 claw-free cap odd anti-hole-free cap tripartite 
 claw-free cap odd-hole-free cap tripartite 
 claw-free cap perfect 
 claw-free cap upper domination perfect 
 clique 
 clique separable 
 clique-Helly 
 clique-Helly cap clique-chordal 
 clique-Helly cap dismantlable 
 clique-Helly cap dismantlable cap reflexive 
 clique-chordal 
 clique-perfect 
 clique-perfect cap triangle-free 
 cliquewidth 2 
 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-bipartite 
 co-bithreshold 
 co-bithreshold cap split 
 co-bounded tolerance 
 co-charming 
 co-chordal 
 co-chordal cap comparability 
 co-chordal cap superperfect 
 (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-comparability 
 co-comparability cap comparability 
 co-comparability cap tolerance 
 co-comparability cup comparability 
 co-comparability graphs of posets of interval dimension 2 
 co-comparability graphs of posets of interval dimension 2, height 1 
 co-convex-round 
 (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,house)-free 
 (co-fork,odd anti-cycle)-free 
 (co-gem,gem)-free 
 (co-gem,house)-free 
 co-gem-free 
 co-hereditary clique-Helly 
 co-interval 
 co-interval cap cograph 
 co-interval cap cograph cap interval 
 co-interval cap interval 
 co-interval cup interval 
 co-line graphs of bipartite graphs 
 co-normal 
 (co-paw,odd anti-hole)-free 
 (co-paw,paw)-free 
 co-perfectly orderable 
 co-permutation 
 co-probe cograph 
 co-probe threshold 
 co-strongly chordal 
 co-sun-free 
 co-threshold tolerance 
 co-tolerance 
 co-trapezoid 
 co-trivially perfect 
 co-trivially perfect cap trivially perfect 
 cograph 
 cograph cap interval 
 cograph cap split 
 cograph contraction 
 comparability 
 comparability cap split 
 comparability cap 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 posets of interval dimension 2 
 comparability graphs of posets of interval dimension 2, height 1 
 comparability graphs of semiorders 
 comparability graphs of series-parallel posets 
 comparability graphs of threshold orders 
 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 
 cycle-bicolorable 
 cycle-free 
 diametral path 
 (diamond,odd-hole)-free 
 diamond-free 
 diamond-free cap perfect 
 difference 
 directed path 
 disk 
 disk-Helly 
 dismantlable 
 distance-hereditary 
 dominating pair 
 domination 
 domination perfect 
 domination perfect cap planar 
 domination perfect cap triangle-free 
 domino 
 (domino,gem,house)-free 
 (domino,gem,house)-free cap pseudo-modular 
 (domino,hole,odd-cycle)-free 
 domino-free 
 domino-free cap modular 
 domishold 
 doubly chordal 
 dually chordal 
 even anti-cycle-free 
 even anti-hole-free 
 even-cycle-free 
 even-hole-free 
 even-hole-free cap probe chordal 
 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 
 gem-free 
 generalized strongly chordal 
 genus 0 
 genus 1 
 geodetic 
 good 
 graceful 
 grid 
 grid intersection 
 gridline 
 half-disk Helly 
 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 clique-Helly 
 hereditary disk-Helly 
 hereditary dismantlable 
 hereditary dually chordal 
 hereditary homogeneously orderable 
 hereditary maximal clique irreducible 
 hereditary median 
 hereditary modular 
 hereditary perfect elimination bipartite 
 hereditary weakly modular 
 (hole,odd-cycle)-free 
 hole-free 
 homogeneously orderable 
 homogeneously representable 
 (house,hole,domino,sun)-free 
 house-free 
 house-free cap weakly chordal 
 i-triangulated 
 indifference 
 induced-hereditary pseudo-modular 
 intersection graph of nested intervals 
 intersection graphs of parallelograms (squares) 
 interval 
 interval 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-HH-free 
 isometric-hereditary pseudo-modular 
 k-leaf power, fixed k 
 k-polygon 
 k-tree, fixed k 
 kernel solvable 
 line 
 line cap perfect 
 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 hypergraphs of rank 3 
 line graphs of multigraphs without triangles 
 line graphs of triangle-free graphs 
 linear arboricity <= 2 
 linear domino 
 locally perfect 
 matrogenic 
 matroidal 
 maxibrittle 
 maximal clique irreducible 
 maximal outerplanar 
 median 
 middle 
 minimally imperfect 
 modular 
 modular cap open-neighbourhood-Helly 
 multitolerance 
 murky 
 nK2-free, fixed n 
 nearly bipartite 
 neighbourhood perfect 
 neighbourhood-Helly 
 neighbourhood-Helly cap pseudo-modular cap reflexive 
 normal 
 odd anti-cycle-free 
 (odd anti-hole,odd-hole)-free 
 odd anti-hole-free 
 odd co-sun-free 
 (odd-cycle,star1,2,3,sunlet4)-free 
 (odd-cycle,star1,2,3)-free 
 odd-cycle-free 
 (odd-hole,paw)-free 
 odd-hole-free 
 odd-hole-free cap planar 
 odd-hole-free cap pretty 
 odd-sun-free 
 open-neighbourhood-Helly 
 opposition 
 outerplanar 
 (p,q)-colorable 
 (p,q<=2)-colorable 
 p-connected 
 p-tree 
 parity 
 partial 2-tree 
 partial 3-tree 
 partial 4-tree 
 partial bar visibility 
 partial grid 
 partial k-tree, fixed k 
 partial rectangle visibility 
 partitionable 
 partner-limited 
 paw-free 
 paw-free cap perfect 
 perfect 
 perfect cap planar 
 perfect cap split-neighbourhood 
 perfect cap triangle-free 
 perfect connected-dominant 
 perfect elimination bipartite 
 perfectly 1-transversable 
 perfectly contractile 
 perfectly orderable 
 permutation 
 permutation cap split 
 planar 
 planar of degree 3 
 polar 
 power-chordal 
 preperfect 
 pretty 
 probe Gallai 
 probe Meyniel 
 probe P4-reducible 
 probe P4-sparse 
 probe chordal 
 probe chordal cap weakly chordal 
 probe co-comparability 
 probe co-trivially perfect 
 probe co-trivially perfect cap probe trivially perfect 
 probe cograph 
 probe comparability 
 probe distance-hereditary 
 probe interval 
 probe interval cap tree 
 probe interval bigraph 
 probe permutation 
 probe split 
 probe threshold 
 probe threshold cap split 
 probe trivially perfect 
 probe unit interval 
 proper circular arc 
 proper interval 
 proper tolerance 
 pseudo-median 
 pseudo-modular 
 pseudo-modular cap triangle-free 
 pseudo-split 
 ptolemaic 
 ptolemaic cap weakly geodetic 
 (q, q-3), fixed q>= 7 
 (q,q-4), fixed q 
 (q,t) 
 quasi-Meyniel 
 quasi-brittle 
 quasi-median 
 quasi-parity 
 quasi-threshold 
 quasitriangulated 
 rectangle visibility 
 reflexive 
 semi-P4-sparse 
 series-parallel 
 short-chorded 
 skeletal 
 slender 
 slightly triangulated 
 slim 
 spider graph 
 split 
 split cap strongly chordal 
 split cap superperfect 
 split cap threshold signed 
 split-neighbourhood 
 split-perfect 
 square of tree 
 strict 2-threshold 
 strict quasi-parity 
 string 
 strong domination perfect 
 strong tree-cograph 
 strongly chordal 
 strongly orderable 
 strongly perfect 
 subtree filament 
 subtree overlap 
 sun-free 
 sun-free cap weakly chordal 
 superbrittle 
 superfragile 
 superperfect 
 thick tree 
 thickness <= 2 
 threshold 
 threshold signed 
 threshold tolerance 
 tolerance 
 toroidal 
 totally unimodular 
 trapezoid 
 tree 
 tree-cograph 
 tree-perfect 
 triangle-free 
 tripartite 
 trivially perfect 
 unbreakable 
 undirected path 
 unigraph 
 unimodular 
 unit bar visibility 
 unit circular arc 
 unit disk 
 unit interval 
 unit tolerance 
 upper domination perfect 
 upper irredundance perfect 
 very strongly perfect 
 visibility 
 weak bar visibility 
 weak bipolarizable 
 weak bisplit 
 weak dominating pair 
 weak rectangle visibility 
 weakly chordal 
 weakly geodetic 
 weakly modular 
 well covered 
 wing-triangulated