edgeless

providers: ISGCI

Definition: A graph with no edges.

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	magenta■	exclusion	unknown to HOPS
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	red■	exclusion	upper bound
boxicity	red■	exclusion	upper bound
branch width	red■	exclusion	upper bound
c-closure	red■	exclusion	upper bound
carving-width	red■	exclusion	upper bound
chordal	red■	exclusion	upper bound
chordality	red■	exclusion	upper bound
chromatic number	red■	exclusion	upper bound
clique cover number	blue■	exclusion	unbounded
clique-tree-width	red■	exclusion	upper bound
clique-width	red■	exclusion	upper bound
cluster	red■	exclusion	inclusion
co-cluster	red■	exclusion	inclusion
cograph	red■	exclusion	upper bound
complete	blue■	exclusion	exclusion
connected	blue■	exclusion	exclusion
contraction complexity	red■	exclusion	upper bound
cutwidth	red■	exclusion	upper bound
cycle	blue■	exclusion	exclusion
cycles	blue■	exclusion	exclusion
d-path-free	red■	exclusion	upper bound
degeneracy	red■	exclusion	upper bound
degree treewidth	red■	exclusion	upper bound
diameter	red■	exclusion	upper bound
diameter+max degree	red■	exclusion	upper bound
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	blue■	exclusion	unbounded
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	blue■	exclusion	unbounded
edge clique cover number	magenta■	exclusion	unknown to HOPS
edge connectivity	red■	exclusion	upper bound
edgeless	yellow■	equal	equal
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	red■	exclusion	inclusion
linear NLC-width	red■	exclusion	upper bound
linear rank-width	red■	exclusion	upper bound
maximum clique	red■	exclusion	upper bound
maximum degree	red■	exclusion	upper bound
maximum independent set	blue■	exclusion	unbounded
maximum induced matching	red■	exclusion	upper bound
maximum leaf number	magenta■	exclusion	unknown to HOPS
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	red■	exclusion	upper bound
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	blue■	exclusion	exclusion
stars	red■	exclusion	inclusion
topological bandwidth	magenta■	exclusion	unknown to HOPS
tree	blue■	exclusion	exclusion
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

2017 Graph Theory by Diestel
- page 5 : edgeless – A vertex of degree $0$ is \emph{isolated}.
unknown source
- edgeless upper bounds vertex cover by a constant
- graph class edgeless has unbounded domination number
- edgeless upper bounds maximum matching by a constant
assumed
- graph class edgeless is included in graph class linear forest
- graph class linear forest is not included in graph class edgeless
- graph class edgeless is included in graph class stars
- graph class stars is not included in graph class edgeless
- graph class edgeless is included in graph class co-cluster
- graph class co-cluster is not included in graph class edgeless
- graph class edgeless is included in graph class cluster
- graph class cluster is not included in graph class edgeless
- edgeless upper bounds distance to edgeless by a constant – by definition
- edgeless upper bounds bounded components by a constant – By definition
- graph class edgeless is not included in graph class connected – By definition
- graph class edgeless is not included in graph class cycles – By definition
- edgeless is equivalent to edgeless – assumed