connected

equivalent to: connected

Relations

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

Results

assumed
- connected – A graph is connected if there is a path between any pair of its vertices.
- graph class complete is included in graph class connected – by definition
- graph class tree is included in graph class connected – by definition
- graph class path is included in graph class connected – by definition
- graph class star is included in graph class connected – by definition
- graph class cycle is included in graph class connected – by definition
- graph class grid is included in graph class connected
- graph class connected is not included in graph class grid