distance to stars

Relations

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

Results

unknown source
- distance to stars upper bounds treedepth by a linear function – First, treedepth removes vertices of the modulator, remainder has treedepth $2$
assumed
- graph class stars has constant distance to stars – by definition