disconnected

Relations

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

Results

assumed
- disconnected upper bounds distance to disconnected by a constant – by definition
- disconnected is equivalent to disconnected – assumed