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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 ∩ 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
(2,2)-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,Cn+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-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,K1,4,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,K1,4,K5 - e,claw ∪ K1,co-butterfly,co-cricket,co-dart,co-gem)-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,K3,3,K3,3+e,P4,2P3)-free
(2K2,P3,triangle)-free
(2K2,P3)-free
(2K2,P4,2P3)-free
(2K2,P4,co-dart)-free
(2K2,P4)-free
(2K2,2P3,C6)-free
(2K2,C6,C8,K1,4,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,K3,3-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,K3,3-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,K3,3-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,K3,3-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,K2,3,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,K2,3,K3 ∪ P3,X84,3K2,C4 ∪ P2,C6,P2 ∪ P4,P6,X18,X5,co-antenna,co-domino,co-fish)-free
(2K3,2P3,Cn+4,K3 ∪ P3)-free
(2K3,3K1,A,H,X45)-free
(2K3,4K1,C7,X38,X39,W4 ∪ K1,W5,X86,X87,X88,X89,X90,butterfly ∪ K1,diamond)-free
(2K3,Cn+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,K2,3,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,C6)-free
(2P3,C4,P4)-free
(2P3,P4)-free
(2P3,triangle)-free
2P3-free
(2P4,A,C5,C6,C7,E,K3,3-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,K3,4-e,T2,X18,X92,X93)-free
(3K1,C5,K5 - e,C6 ∪ K1,C7,K3,3 ∪ K1,K3,3-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,K1,5)-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,K3,3,K3,3+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,Cn+4)-free
(3P3,Cn+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,Cn+4,K5 - e,S3,X100,X101,X102,H,K3 ∪ 2K1)-free
(4-fan,Cn+4,K5 - e,S3,H,K3 ∪ 2K1)-free
(4-fan,K1,4,W4,W5,A ∪ K1,co-fork ∪ K1,gem ∪ K1,net ∪ K1)-free
4-leaf power
4-regular
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,K4)-free
(4K1,P4)-free
(4K1,Cn+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 ∩ planar
(6,1)-chordal
(6,1)-chordal ∩ bipartite
(6,1)-even-chordal
(6,2)
(6,2)-chordal
(6,2)-chordal ∩ bipartite
(6,3)
(6-fan,C4 ∪ P2,C5,C6 ∪ K1,C7,K2 ∪ K3,K2,3,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)
(7,5)
(8,4)
(9,6)
(A ∪ K1,K1,4,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,K2 ∪ K3,K3,3,K3,3+e,K3,3-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,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,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
(A,3P3,Cn+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-VPG
B0-VPG ∩ bipartite
B0-VPG ∩ chordal
B0-VPG ∩ strongly chordal
B0-VPG ∩ triangle-free
B1-VPG
B1-VPG contact
B2-VPG
B3-VPG
(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,C6,C8,T2,X3)-free
BW3-free
BW3-free ∩ modular
Berge
Berge ∩ bull-free
Berge ∩ claw-free
Birkhoff
Bk-VPG
Bouchet
(C4 ∪ P2,C5,C6,K2 ∪ K3,K2,3,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,K1,4,X85,triangle)-free
(C4,C5,C6,C7,C8,H,X85,triangle)-free
(C4,C5,C6,C7,C8,H,X85,triangle)-free ∩ K1,4-free
(C4,C5,C6,C7,C8,K1,4,K5,K5 - e,K3 ∪ 2K1,P3 ∪ 2K1,claw ∪ K1,butterfly,cricket,dart,gem)-free
(C4,C5,C6,C7,C8,K1,4,K5,K5 - e,K3 ∪ 2K1,P3 ∪ 2K1,claw ∪ K1,butterfly,cricket,dart,gem)-free ∩ planar
(C4,C5,C6,C7,C8,XC11,claw,diamond)-free
(C4,C5,C6,C7,C8)-free
(C4,C5,C6,C7,C8)-free ∩ maximum degree 3 ∩ planar
(C4,C5,C6,S3)-free
(C4,C5,K4,diamond)-free
(C4,C5,K4,diamond)-free ∩ planar
(C4,C5,T2)-free
(C4,C5)-free
(C4,C5)-free ∩ Helly
(C4,C5)-free ∩ cop-win
(C4,C6,C8,K1,4,odd-cycle)-free
(C4,C6,C8,K1,4,odd-cycle)-free ∩ planar
(C4,C6,odd-cycle)-free
(C4,K4,claw,diamond)-free
(C4,P4,dart)-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 ∩ induced-hereditary pseudo-modular
C4-free ∩ odd-signable
C4-free ∩ perfect
(C5,C6 ∪ K1,C7,K3,3 ∪ K1,K3,3-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,K2,3,P,P2 ∪ P3,P5,P,P2 ∪ P3,co-fork,fork,house)-free
(C5,K3,3-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,Cn+4 ∪ K1,T2,net ∪ K1,co-diamond,co-domino,co-eiffeltower,co-twin-C5)-free
(C6,K2 ∪ K3,X37,X90,Cn+4 ∪ K1,T2,Wn+4,X31,co-XF2n+1,co-XF3n,co-domino,co-twin-C5)-free
(C6,K3,3+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,Cn+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
(Cn+3 ∪ K1,diamond,paw)-free
(Cn+4 ∪ K1,C(n,k),W4,odd-cycle ∪ K1,even anti-hole,net)-free
(Cn+4 ∪ K1,C(n,k),X42,T2,X2,X3,odd-cycle ∪ K1,even anti-hole,net)-free
(Cn+4 ∪ K1,K2,3,T2,Wn+4,X31,XF2n+1,XF3n,C6,X37,X90,domino,twin-C5)-free
(Cn+4 ∪ K1,K2,3,T2,C6,X103,X37,X88,X90,diamond,domino,eiffeltower,net ∪ K1,twin-C5)-free
(Cn+4 ∪ K1,K2,3,T2,X90,domino,paw,twin-C5)-free
(Cn+4 ∪ K1,S3 ∪ K1,X42,T2,X2,X3,odd-cycle ∪ K1,even anti-hole,net)-free
(Cn+4 ∪ K1,S3,W4,W5,C6,claw,net)-free
(Cn+4 ∪ K1,S3,W4,odd-cycle ∪ K1,even anti-hole,net)-free
(Cn+4,H)-free
(Cn+4,K4)-free
(Cn+4,P5,bull)-free
(Cn+4,P5,claw,gem)-free
(Cn+4,S3 ∪ K1,X103,claw,eiffeltower,net ∪ K1)-free
(Cn+4,S3 ∪ 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,X102,X204,P3 ∪ 2K1,gem)-free
(Cn+4,X59,longhorn)-free
(Cn+4,XF12n+3,XF62n+2,X34,X36,co-XF2n+1,co-XF3n)-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,Cn+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
(Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X36,XF12n+3,XF2n+1,XF3n,XF4n,XF52n+3,XF62n+2,Cn+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
(Cn+6,X37,claw,co-antenna,net,sun)-free
(Cn+6,odd-cycle)-free
Cn+6-free
Cn+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
Fn grid
Gabriel
Gallai
Gallai-perfect
(H,K3 ∪ 2K1,Cn+4,K5 - e,X100,X101,X102,co-4-fan,net)-free
(H,K3 ∪ 2K1,Cn+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
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 ∩ perfect
Helly circular arc ∩ self-clique
Helly subtree
Hilbertian
Hn,q grid
(K1,4,P,P5,fork)-free
(K1,4,P5)-free
(K1,4,diamond)-free
(K1,4,odd-cycle)-free
(K1,4,odd-cycle)-free ∩ planar
(K1,4,paw)-free
K1,4-free
K1,4-free ∩ almost claw-free ∩ locally connected
K1,4-free ∩ well covered
(K1,5,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,Cn+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
(K2,3,K4)-minor-free
(K2,3,P,P5,X163,X95,diamond)-free
(K2,3,P,P5)-free
(K2,3,P,hole)-free
(K2,3,P4,co-butterfly)-free
(K2,3,P5)-free
(K2,3,X37,X38,diamond,domino,house,twin-C5)-free
(K2,3,diamond)-free
(K2,3,diamond)-free ∩ weakly modular
K2,3-free
K2,3-free ∩ hereditary modular
K2-free
(K3 ∪ P3,C6,P,P7,X37,X41)-free
(K3,3,3,Cn+4)-free
(K3,3,K3,3+e,2P3,Cn+4)-free
(K3,3,K4,W4 ∪ K1,W5,X86,X87,X88,X89,X90,C7,X38,X39,butterfly ∪ K1,co-diamond)-free
(K3,3,K5)-minor-free
(K3,3,P5)-free
(K3,3,Cn+4)-free
(K3,3-e,P5,X98)-free
(K3,3-e,P5,X99)-free
(K3,3-e,P5)-free
K3-minor-free
(K4,4,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 ∩ perfect
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
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,star1,2,3)-free
(P,star1,2,4)-free
(P,star1,2,5)-free
P-free
(P2 ∪ P3,house)-free
(P2 ∪ P4,triangle)-free
P2 ∪ P4-free
(P3 ∪ 2K1,Cn+4,X102,X204,co-gem)-free
(P3,triangle)-free
P3-free
(P4,2P3)-free
(P4,co-cycle)-free
(P4,cycle)-free
(P4,triangle)-free
P4-bipartite
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,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,C6)-free ∩ weakly chordal
(P5,P,anti-hole)-free
(P5,P,gem)-free
(P5,P2 ∪ P3)-free
(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,triangle)-free
P6-free
P6-free ∩ chordal bipartite
P6-free ∩ tripartite
(P7,odd-cycle,star1,2,3,sunlet4)-free
(P7,odd-cycle,star1,2,3)-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,Cn+4 ∪ K1,C(n,k),X42,even-hole,odd-cycle ∪ K1)-free
(S3,T2,X2,X3,Cn+4 ∪ K1,S3 ∪ K1,X42,even-hole,odd-cycle ∪ K1)-free
(S3,3K2,E,P2 ∪ P4,odd anti-hole,odd-hole)-free
(S3,3K2,E,P2 ∪ P4)-free
(S3,3K2,E,odd-hole)-free
(S3,3K2,E,odd-hole)-free ∩ line
(S3,Cn+4 ∪ K1,C(n,k),W4,even-hole,odd-cycle ∪ K1)-free
(S3,Cn+4,S3 ∪ K1,co-claw)-free
(S3,Cn+4,T2)-free
(S3,Cn+4,co-claw,net)-free
(S3,Cn+4,co-claw)-free
(S3,Cn+4,net)-free
(S3,Cn+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,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
(T3,cycle)-free
Urquhart
V-perfect
VPG
W2n+3-free
(W4,W5,butterfly)-free
(W4,claw,gem,odd-hole)-free
(W4,claw,gem)-free
(W4,claw)-free
(W4,gem)-free
(W4,gem)-free ∩ short-chorded
Welsh-Powell opposition
Welsh-Powell perfect
Wn+4-free
X-chordal
X-chordal ∩ X-conformal ∩ bipartite
X-chordal ∩ bipartite
X-conformal
X-conformal ∩ bipartite
X-conformal ∩ bipartite ∩ hereditary X-chordal
X-star-chordal
(X103,Cn+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,Cn+4,co-XF12n+3,co-XF62n+2)-free
(X37,diamond,even-cycle)-free
(X38,gem,house)-free
(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,Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X35,X36,co-XF2n+1,co-XF3n,co-XF4n,odd-hole)-free
(XF12n+3,XF52n+3,XF62n+2,T2,X2,X3,X30,X31,X32,X33,X34,X35,X36,anti-hole,co-XF2n+1,co-XF3n,co-XF4n,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
cal C(G)-perfect
cal P3-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
(Cn+3 ∪ K1,co-diamond,co-paw)-free
(Cn+4,H)-free
(Cn+4,T2,X31,co-XF2n+1,co-XF3n)-free
(Cn+4,T2,co-XF2n+1)-free
(Cn+4,X59,co-longhorn)-free
(Cn+4,bull,co-dart,co-gem)-free
(Cn+4,bull,house)-free
(Cn+4,co-claw,co-gem,house)-free
(Cn+4,co-claw,co-gem)-free
(Cn+4,co-claw)-free
(Cn+4,co-diamond)-free
(Cn+4,co-gem)-free
(Cn+4,co-sun)-free
(Cn+4,net)-free
(Cn+4,odd co-sun)-free
Cn+4-free
(Cn+6,T2,X2,X3,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39,X40,X41,co-XF2n+1,co-XF3n,co-XF4n)-free
(Cn+6,odd anti-cycle)-free
Cn+6-free
Cn+7-free
(E,P)-free
(E,odd anti-cycle)-free
E-free
(K1,4,P,co-fork,house)-free
(K1,4,co-diamond)-free
(K1,4,co-paw)-free
(K1,4,house)-free
(K1,4,odd anti-cycle)-free
K1,4-free
K2 ∪ claw-free
(P,P7)-free
(P,P8)-free
(P,T2)-free
(P,star1,2,3)-free
(P,butterfly,fork,gem)-free
(P,co-star1,2,4)-free
(P,co-star1,2,5)-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,star1,2,3,sunlet4,odd anti-cycle)-free
(P7,star1,2,3,odd anti-cycle)-free
(P7,odd anti-cycle)-free
P7-free
(T2,co-cycle)-free
(T3,X81,co-cycle)-free
(T3,co-cycle)-free
W2n+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
Wn+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
(star1,2,3,sunlet4,odd anti-cycle)-free
(star1,2,3,odd anti-cycle)-free
τk-perfect for all k >= 2
absolute bipartite retract
absolute reflexive retract
absolutely perfect
absorbantly perfect
adjoint
adjoint ∩ partial directed line
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 ∩ 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 ∪ line graphs of bipartite graphs
bipartite chain
bipartite permutation
bipartite tolerance
biplanar
bipolarizable
bisplit
bisplit ∩ triangle-free
bithreshold
bitolerance
block
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
(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 ∩ 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 ∩ 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 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 ∩ 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-bipartite
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-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
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 ∩ 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 line
directed path
disjoint union of stars
disk
disk contact
disk-Helly
dismantlable
distance regular
distance regular of diameter 2
distance-hereditary
dominating pair
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
gem-free
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-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 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-starlike
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 hypergraphs of rank 3
line graphs of multigraphs without triangles
line graphs of triangle-free graphs
linear NLC-width 1
linear arboricity <= 2
linear cliquewidth 2
linear domino
linear domino ∩ maximum degree 4
linearly convex triangular grid graph
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
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,star1,2,3,sunlet4)-free
(odd-cycle,star1,2,3)-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 directed line
partial grid
partial k-tree, fixed k
partial rectangle visibility
partitionable
partner-limited
path orderable
paw-free
paw-free ∩ perfect
perfect
perfect ∩ planar
perfect ∩ split-neighbourhood
perfect ∩ triangle-free
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 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-adjoint
quasi-brittle
quasi-line
quasi-median
quasi-parity
quasi-threshold
quasitriangulated
rectagraph
rectangle intersection
rectangle visibility
reflexive
relative neighbourhood graph
rigid circuit
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
strict 2-threshold
strict B1-VPG contact
strict quasi-parity
strictly clique irreducible
string
strong asteroid free
strong domination perfect
strong tree-cograph
strongly 3-colorable
strongly chordal
strongly circular perfect
strongly even-signable
strongly odd-signable
strongly orderable
strongly perfect
strongly regular
subhamiltonian
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 tolerance
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 chordal
weakly geodetic
weakly median
weakly modular
well covered
well-dominated
wing-triangulated