distance to planar

Relations

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

Results

2022 Expanding the Graph Parameter Hierarchy by Tran
- page 37 : distance to planar upper bounds twin-width by an exponential function – Theorem 6.4. Distance to Planar strictly upper bounds Twin-width.
- page 37 : bounded twin-width does not imply bounded distance to planar – Theorem 6.4. Distance to Planar strictly upper bounds Twin-width.
unknown source
- bounded bounded components does not imply bounded distance to planar – By a disjoint union of many $K_5$ graphs.
Comparing Graph Parameters by Schröder
- page 21 : bounded bandwidth does not imply bounded distance to planar – Proposition 3.13
- page 21 : bounded treedepth does not imply bounded distance to planar – Proposition 3.13
- page 23 : bounded distance to planar does not imply bounded clique-width – Proposition 3.17
- page 33 : bounded genus does not imply bounded distance to planar – Proposition 3.34
assumed
- graph class planar has constant distance to planar – by definition