star

Definition: Contains only edges that connect a vertex to every other vertex.

Relations

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

Results

2010 Comparing 17 graph parameters by Sasák
- page 30 : graph class star has unbounded carving-width – Corollary 2.21 Carving-width of a star is $n-1$.
unknown source
- star upper bounds vertex cover by a constant – trivially
- star upper bounds h-index by a constant – trivially
- graph class star has unbounded maximum degree – trivially
- star upper bounds maximum matching by a constant
assumed
- star upper bounds connected by a constant – by definition
- star upper bounds stars by a constant – by definition
- graph class star is included in graph class tree
- graph class tree is not included in graph class star
- star is equivalent to star – assumed