excluded minor

Definition: There is a finite family of graphs $H$ such that the graph class does not contain any graph of $H$ is its minor.

Relations

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

Results

assumed
- excluded minor is equivalent to excluded minor – assumed
unknown source
- excluded minor upper bounds excluded top-minor by a constant
- excluded planar minor upper bounds excluded minor by a constant
- planar upper bounds excluded minor by a constant
- genus upper bounds excluded minor by a computable function