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(0,2)-graph ∩ bipartite
1-DIR
1-string
2-DIR
2-SEG
2-connected ∩ cubic ∩ planar
2-outerplanar
2-strongly regular ∩ planar
2-subdivision ∩ planar
3-DIR
3-tree ∩ planar
4-regular ∩ hamiltonian ∩ planar
4-regular ∩ planar
(5-pan,T2,X172)-free ∩ planar
5-regular ∩ hamiltonian ∩ planar
5-regular ∩ planar
Apollonian network
(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)-free ∩ maximum degree 3 ∩ planar
(C4,C5,K4,diamond)-free ∩ planar
(C4,C6,C8,K1,4,odd-cycle)-free ∩ planar
(C4,triangle)-free ∩ planar
CONV
Delaunay
E-free ∩ planar
Gabriel
Halin
(K1,4,odd-cycle)-free ∩ planar
Laman ∩ planar
PURE-2-DIR
PURE-3-DIR
PURE-k-DIR
SEG
Urquhart
(XC11,odd-cycle)-free ∩ planar
(XC12,triangle)-free ∩ planar
apex
bar visibility
bipartite ∩ cubic ∩ planar
bipartite ∩ girth >=9 ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 3 ∩ planar
bipartite ∩ maximum degree 4 ∩ planar
bipartite ∩ planar
biplanar
chordal ∩ hamiltonian ∩ planar
chordal ∩ maximal planar
chordal ∩ planar
co-planar
cubic ∩ hamiltonian ∩ planar
cubic ∩ planar
d-trapezoid
domination perfect ∩ planar
grid intersection
gridline
hamiltonian ∩ planar
hole-free ∩ planar
homothetic triangle contact
interval filament
k-DIR
k-SEG
k-outerplanar
line graphs of planar cubic bipartite graphs
maximal outerplanar
maximal planar
maximum degree 3 ∩ planar ∩ triangle-free
median ∩ planar
odd-hole-free ∩ planar
outerplanar
partial 3-tree ∩ planar
perfect ∩ planar
planar
planar ∩ strongly regular
planar ∩ triangle-free
planar of maximum degree 3
planar of maximum degree 4
polyhedral
rectangle visibility
relative neighbourhood graph
solid grid graph
solid triangular grid graph
string
subhamiltonian
subtree filament
thickness <= 2
triangle contact
triangular grid graph
weak bar visibility
weak rectangle visibility