excluded planar minor

Definition: There is a finite family of graphs $H$, with at least one graph of $H$ being planar, such that the graph class does not contain any graph of $H$ is its minor.

Relations

Other		Relation from	Relation to
acyclic chromatic number	red■	avoids	upper bound
admissibility	red■	avoids	upper bound
arboricity	red■	avoids	upper bound
average degree	red■	avoids	upper bound
average distance	magenta■	avoids	unknown to HOPS
bandwidth	gray■	unknown to HOPS	unknown to HOPS
bipartite	magenta■	avoids	unknown to HOPS
bipartite number	magenta■	avoids	unknown to HOPS
bisection bandwidth	magenta■	avoids	unknown to HOPS
block	magenta■	avoids	unknown to HOPS
book thickness	red■	avoids	upper bound
boolean width	red■	avoids	upper bound
bounded components	gray■	unknown to HOPS	unknown to HOPS
bounded expansion	red■	avoids	upper bound
boxicity	red■	avoids	upper bound
branch width	orange■	unknown to HOPS	upper bound
c-closure	magenta■	avoids	unknown to HOPS
carving-width	gray■	unknown to HOPS	unknown to HOPS
chi-bounded	red■	avoids	upper bound
chordal	magenta■	avoids	unknown to HOPS
chordality	red■	avoids	upper bound
chromatic number	red■	avoids	upper bound
clique cover number	magenta■	avoids	unknown to HOPS
clique-tree-width	red■	avoids	upper bound
clique-width	red■	avoids	upper bound
cluster	magenta■	avoids	unknown to HOPS
co-cluster	magenta■	avoids	unknown to HOPS
cograph	magenta■	avoids	unknown to HOPS
complete	magenta■	avoids	unknown to HOPS
connected	magenta■	avoids	unknown to HOPS
contraction complexity	gray■	unknown to HOPS	unknown to HOPS
cutwidth	gray■	unknown to HOPS	unknown to HOPS
cycle	gray■	unknown to HOPS	unknown to HOPS
cycles	gray■	unknown to HOPS	unknown to HOPS
d-admissibility	red■	avoids	upper bound
d-path-free	gray■	unknown to HOPS	unknown to HOPS
degeneracy	red■	avoids	upper bound
degree treewidth	gray■	unknown to HOPS	unknown to HOPS
diameter	magenta■	avoids	unknown to HOPS
diameter+max degree	gray■	unknown to HOPS	unknown to HOPS
distance to bipartite	magenta■	avoids	unknown to HOPS
distance to block	magenta■	avoids	unknown to HOPS
distance to bounded components	gray■	unknown to HOPS	unknown to HOPS
distance to chordal	magenta■	avoids	unknown to HOPS
distance to cluster	magenta■	avoids	unknown to HOPS
distance to co-cluster	magenta■	avoids	unknown to HOPS
distance to cograph	magenta■	avoids	unknown to HOPS
distance to complete	magenta■	avoids	unknown to HOPS
distance to edgeless	gray■	unknown to HOPS	unknown to HOPS
distance to forest	gray■	unknown to HOPS	unknown to HOPS
distance to interval	magenta■	avoids	unknown to HOPS
distance to linear forest	gray■	unknown to HOPS	unknown to HOPS
distance to maximum degree	magenta■	avoids	unknown to HOPS
distance to outerplanar	gray■	unknown to HOPS	unknown to HOPS
distance to perfect	magenta■	avoids	unknown to HOPS
distance to planar	magenta■	avoids	unknown to HOPS
distance to stars	gray■	unknown to HOPS	unknown to HOPS
domatic number	red■	avoids	upper bound
domination number	magenta■	avoids	unknown to HOPS
domino treewidth	gray■	unknown to HOPS	unknown to HOPS
edge clique cover number	magenta■	avoids	unknown to HOPS
edge connectivity	red■	avoids	upper bound
edge-cut width	gray■	unknown to HOPS	unknown to HOPS
edge-treewidth	gray■	unknown to HOPS	unknown to HOPS
edgeless	gray■	unknown to HOPS	unknown to HOPS
excluded minor	red■	avoids	upper bound
excluded planar minor	yellow■	equal	equal
excluded top-minor	red■	avoids	upper bound
feedback edge set	gray■	unknown to HOPS	unknown to HOPS
feedback vertex set	gray■	unknown to HOPS	unknown to HOPS
flip-width	red■	avoids	upper bound
forest	gray■	unknown to HOPS	unknown to HOPS
genus	magenta■	avoids	unknown to HOPS
grid	magenta■	avoids	unknown to HOPS
h-index	magenta■	avoids	unknown to HOPS
interval	magenta■	avoids	unknown to HOPS
iterated type partitions	magenta■	avoids	unknown to HOPS
linear clique-width	magenta■	avoids	unknown to HOPS
linear forest	gray■	unknown to HOPS	unknown to HOPS
linear NLC-width	magenta■	avoids	unknown to HOPS
linear rank-width	magenta■	avoids	unknown to HOPS
maximum clique	red■	avoids	upper bound
maximum degree	magenta■	avoids	unknown to HOPS
maximum independent set	magenta■	avoids	unknown to HOPS
maximum induced matching	magenta■	avoids	unknown to HOPS
maximum leaf number	gray■	unknown to HOPS	unknown to HOPS
maximum matching	gray■	unknown to HOPS	unknown to HOPS
maximum matching on bipartite graphs	gray■	unknown to HOPS	unknown to HOPS
merge-width	red■	avoids	upper bound
mim-width	red■	avoids	upper bound
minimum degree	red■	avoids	upper bound
mm-width	orange■	unknown to HOPS	upper bound
modular-width	magenta■	avoids	unknown to HOPS
module-width	red■	avoids	upper bound
monadically dependent	red■	avoids	upper bound
monadically stable	red■	avoids	upper bound
neighborhood diversity	magenta■	avoids	unknown to HOPS
NLC-width	red■	avoids	upper bound
NLCT-width	red■	avoids	upper bound
nowhere dense	red■	avoids	upper bound
odd cycle transversal	magenta■	avoids	unknown to HOPS
outerplanar	lime■	upper bound	unknown to HOPS
overlap treewidth	gray■	unknown to HOPS	unknown to HOPS
path	gray■	unknown to HOPS	unknown to HOPS
pathwidth	gray■	unknown to HOPS	unknown to HOPS
pathwidth+maxdegree	gray■	unknown to HOPS	unknown to HOPS
perfect	magenta■	avoids	unknown to HOPS
planar	magenta■	avoids	unknown to HOPS
radius-inf flip-width	red■	avoids	upper bound
radius-r flip-width	red■	avoids	upper bound
rank-width	red■	avoids	upper bound
series-parallel	gray■	unknown to HOPS	unknown to HOPS
shrub-depth	magenta■	avoids	unknown to HOPS
sim-width	red■	avoids	upper bound
size	gray■	unknown to HOPS	unknown to HOPS
slim tree-cut width	gray■	unknown to HOPS	unknown to HOPS
sparse twin-width	red■	avoids	upper bound
star	gray■	unknown to HOPS	unknown to HOPS
stars	gray■	unknown to HOPS	unknown to HOPS
strong coloring number	red■	avoids	upper bound
strong d-coloring number	red■	avoids	upper bound
strong inf-coloring number	orange■	unknown to HOPS	upper bound
topological bandwidth	gray■	unknown to HOPS	unknown to HOPS
tree	gray■	unknown to HOPS	unknown to HOPS
tree-cut width	gray■	unknown to HOPS	unknown to HOPS
tree-independence number	red■	avoids	upper bound
tree-partition-width	gray■	unknown to HOPS	unknown to HOPS
treebandwidth	gray■	unknown to HOPS	unknown to HOPS
treedepth	gray■	unknown to HOPS	unknown to HOPS
treelength	magenta■	avoids	unknown to HOPS
treespan	gray■	unknown to HOPS	unknown to HOPS
treewidth	orange■	unknown to HOPS	upper bound
twin-cover number	magenta■	avoids	unknown to HOPS
twin-width	red■	avoids	upper bound
vertex connectivity	gray■	unknown to HOPS	unknown to HOPS
vertex cover	gray■	unknown to HOPS	unknown to HOPS
vertex integrity	gray■	unknown to HOPS	unknown to HOPS
weak coloring number	red■	avoids	upper bound
weak d-coloring number	red■	avoids	upper bound
weak inf-coloring number	gray■	unknown to HOPS	unknown to HOPS
weakly sparse	red■	avoids	upper bound
weakly sparse and merge width	red■	avoids	upper bound

Results

1986 Graph minors. V. Excluding a planar graph by Robertson, Seymour
- page 2 : excluded planar minor upper bounds treewidth by a constant – (1.5) For every planar graph $H$, there is a number $w$ such that every planar graph with no minor isomorphic to $H$ has tree-wdtih $\le w$
assumed
- excluded planar minor is equivalent to excluded planar minor – assumed
unknown source
- outerplanar upper bounds excluded planar minor by a constant
- excluded planar minor upper bounds excluded minor by a constant