planar

equivalent to: planar

providers: ISGCI

Relations

Other	Relation from	Relation to
acyclic chromatic number	exclusion	constant
arboricity	exclusion	constant
average degree	exclusion	constant
average distance	exclusion	unbounded
bandwidth	exclusion	unbounded
bipartite	exclusion	exclusion
bipartite number	exclusion	unknown to HOPS
bisection bandwidth	exclusion	unbounded
block	exclusion	exclusion
book thickness	exclusion	constant
boolean width	exclusion	unbounded
bounded components	exclusion	unbounded
boxicity	exclusion	constant
branch width	exclusion	unbounded
c-closure	exclusion	unknown to HOPS
carving-width	exclusion	unbounded
chordal	exclusion	exclusion
chordality	exclusion	constant
chromatic number	exclusion	constant
clique cover number	exclusion	unbounded
clique-tree-width	exclusion	unbounded
clique-width	exclusion	unbounded
cluster	exclusion	exclusion
co-cluster	exclusion	exclusion
cograph	exclusion	exclusion
complete	exclusion	exclusion
connected	exclusion	unknown to HOPS
cutwidth	exclusion	unbounded
cycle	inclusion	exclusion
cycles	inclusion	exclusion
d-path-free	exclusion	unbounded
degeneracy	exclusion	constant
degree treewidth	exclusion	unbounded
diameter	exclusion	unbounded
diameter+max degree	exclusion	unbounded
disjoint cycles	inclusion	exclusion
distance to bipartite	exclusion	unbounded
distance to block	exclusion	unbounded
distance to bounded components	exclusion	unbounded
distance to chordal	exclusion	unbounded
distance to cluster	exclusion	unbounded
distance to co-cluster	exclusion	unbounded
distance to cograph	exclusion	unbounded
distance to complete	exclusion	unbounded
distance to edgeless	exclusion	unbounded
distance to forest	exclusion	unbounded
distance to interval	exclusion	unbounded
distance to linear forest	exclusion	unbounded
distance to maximum degree	exclusion	unbounded
distance to outerplanar	exclusion	unbounded
distance to perfect	exclusion	unbounded
distance to planar	exclusion	constant
distance to stars	exclusion	unbounded
domatic number	exclusion	constant
domination number	exclusion	unbounded
edge clique cover number	exclusion	unbounded
edge connectivity	exclusion	constant
edgeless	inclusion	exclusion
feedback edge set	unknown to HOPS	unbounded
feedback vertex set	exclusion	unbounded
forest	inclusion	exclusion
genus	exclusion	constant
girth	exclusion	unbounded
grid	inclusion	exclusion
h-index	exclusion	unbounded
inf-flip-width	exclusion	unbounded
interval	exclusion	exclusion
iterated type partitions	exclusion	unbounded
linear clique-width	exclusion	unbounded
linear forest	inclusion	exclusion
linear NLC-width	exclusion	unbounded
linear rank-width	exclusion	unbounded
maximum clique	exclusion	constant
maximum degree	exclusion	unbounded
maximum independent set	exclusion	unbounded
maximum induced matching	exclusion	unbounded
maximum leaf number	unknown to HOPS	unbounded
maximum matching	exclusion	unbounded
maximum matching on bipartite graphs	unknown to HOPS	unbounded
mim-width	exclusion	unknown to HOPS
minimum degree	exclusion	constant
mm-width	exclusion	unbounded
modular-width	exclusion	unbounded
module-width	exclusion	unbounded
neighborhood diversity	exclusion	unbounded
NLC-width	exclusion	unbounded
NLCT-width	exclusion	unbounded
odd cycle transversal	exclusion	unbounded
outerplanar	inclusion	exclusion
path	inclusion	exclusion
pathwidth	exclusion	unbounded
pathwidth+maxdegree	exclusion	unbounded
perfect	exclusion	exclusion
radius-r flip-width	exclusion	constant
rank-width	exclusion	unbounded
shrub-depth	exclusion	unbounded
sim-width	exclusion	unknown to HOPS
star	inclusion	exclusion
stars	inclusion	exclusion
topological bandwidth	exclusion	unbounded
tree	inclusion	exclusion
tree-independence number	exclusion	unknown to HOPS
treedepth	exclusion	unbounded
treelength	exclusion	unknown to HOPS
treewidth	exclusion	unbounded
twin-cover number	exclusion	unbounded
twin-width	exclusion	constant
vertex connectivity	unknown to HOPS	unknown to HOPS
vertex cover	exclusion	unbounded
vertex integrity	exclusion	unbounded

Results

2017 Graph Theory by Diestel
- page 89 : planar – When we draw a graph on a piece of paper, we naturally try to do this as transparently as possible. One obvious way to limit the mess created by all the lines is to avoid intersections. … Graphs drawn in this way are called \emph{plane graphs}; abstract graphs that can be drawn in this way are called \emph{planar}.
unknown source
- graph class planar has constant genus
- graph class planar has unbounded girth
- graph class planar has unbounded maximum degree
- graph class planar has unbounded distance to perfect
assumed
- graph class outerplanar is included in graph class planar
- graph class planar is not included in graph class outerplanar
- graph class grid is included in graph class planar
- graph class planar is not included in graph class grid
- graph class planar has constant distance to planar – by definition