vertex connectivity

Relations

Other		Relation from	Relation to
acyclic chromatic number	gray■	unknown to HOPS	unknown to HOPS
admissibility	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	gray■	unknown to HOPS	unknown to HOPS
bandwidth	cyan■	unknown to HOPS	exclusion
bipartite	gray■	unknown to HOPS	unknown to HOPS
bipartite number	gray■	unknown to HOPS	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	gray■	unknown to HOPS	unknown to HOPS
bounded components	cyan■	unknown to HOPS	exclusion
bounded expansion	gray■	unknown to HOPS	unknown to HOPS
boxicity	gray■	unknown to HOPS	unknown to HOPS
branch width	gray■	unknown to HOPS	unknown to HOPS
c-closure	blue■	exclusion	exclusion
carving-width	cyan■	unknown to HOPS	exclusion
chi-bounded	gray■	unknown to HOPS	unknown to HOPS
chordal	gray■	unknown to HOPS	unknown to HOPS
chordality	gray■	unknown to HOPS	unknown to HOPS
chromatic number	gray■	unknown to HOPS	unknown to HOPS
clique cover number	gray■	unknown to HOPS	unknown to HOPS
clique-tree-width	gray■	unknown to HOPS	unknown to HOPS
clique-width	gray■	unknown to HOPS	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	cyan■	unknown to HOPS	exclusion
cutwidth	cyan■	unknown to HOPS	exclusion
cycle	cyan■	unknown to HOPS	exclusion
cycles	cyan■	unknown to HOPS	exclusion
d-admissibility	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	cyan■	unknown to HOPS	exclusion
diameter	gray■	unknown to HOPS	unknown to HOPS
diameter+max degree	cyan■	unknown to HOPS	exclusion
distance to bipartite	gray■	unknown to HOPS	unknown to HOPS
distance to block	gray■	unknown to HOPS	unknown to HOPS
distance to bounded components	gray■	unknown to HOPS	unknown to HOPS
distance to chordal	gray■	unknown to HOPS	unknown to HOPS
distance to cluster	gray■	unknown to HOPS	unknown to HOPS
distance to co-cluster	gray■	unknown to HOPS	unknown to HOPS
distance to cograph	gray■	unknown to HOPS	unknown to HOPS
distance to complete	gray■	unknown to HOPS	unknown to HOPS
distance to edgeless	gray■	unknown to HOPS	unknown to HOPS
distance to forest	gray■	unknown to HOPS	unknown to HOPS
distance to interval	gray■	unknown to HOPS	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	gray■	unknown to HOPS	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	gray■	unknown to HOPS	unknown to HOPS
domination number	gray■	unknown to HOPS	unknown to HOPS
domino treewidth	cyan■	unknown to HOPS	exclusion
edge clique cover number	gray■	unknown to HOPS	unknown to HOPS
edge connectivity	gray■	unknown to HOPS	unknown to HOPS
edge-cut width	gray■	unknown to HOPS	unknown to HOPS
edge-treewidth	gray■	unknown to HOPS	unknown to HOPS
edgeless	cyan■	unknown to HOPS	avoids
excluded minor	gray■	unknown to HOPS	unknown to HOPS
excluded planar minor	gray■	unknown to HOPS	unknown to HOPS
excluded top-minor	gray■	unknown to HOPS	unknown to HOPS
feedback edge set	cyan■	unknown to HOPS	exclusion
feedback vertex set	gray■	unknown to HOPS	unknown to HOPS
flip-width	gray■	unknown to HOPS	unknown to HOPS
forest	cyan■	unknown to HOPS	exclusion
genus	gray■	unknown to HOPS	unknown to HOPS
grid	cyan■	unknown to HOPS	exclusion
h-index	gray■	unknown to HOPS	unknown to HOPS
interval	gray■	unknown to HOPS	unknown to HOPS
iterated type partitions	gray■	unknown to HOPS	unknown to HOPS
linear clique-width	gray■	unknown to HOPS	unknown to HOPS
linear forest	cyan■	unknown to HOPS	exclusion
linear NLC-width	gray■	unknown to HOPS	unknown to HOPS
linear rank-width	gray■	unknown to HOPS	unknown to HOPS
maximum clique	gray■	unknown to HOPS	unknown to HOPS
maximum degree	cyan■	unknown to HOPS	exclusion
maximum independent set	gray■	unknown to HOPS	unknown to HOPS
maximum induced matching	gray■	unknown to HOPS	unknown to HOPS
maximum leaf number	cyan■	unknown to HOPS	exclusion
maximum matching	gray■	unknown to HOPS	unknown to HOPS
maximum matching on bipartite graphs	gray■	unknown to HOPS	unknown to HOPS
merge-width	gray■	unknown to HOPS	unknown to HOPS
mim-width	gray■	unknown to HOPS	unknown to HOPS
minimum degree	gray■	unknown to HOPS	unknown to HOPS
mm-width	gray■	unknown to HOPS	unknown to HOPS
modular-width	gray■	unknown to HOPS	unknown to HOPS
module-width	gray■	unknown to HOPS	unknown to HOPS
monadically dependent	gray■	unknown to HOPS	unknown to HOPS
monadically stable	gray■	unknown to HOPS	unknown to HOPS
neighborhood diversity	gray■	unknown to HOPS	unknown to HOPS
NLC-width	gray■	unknown to HOPS	unknown to HOPS
NLCT-width	gray■	unknown to HOPS	unknown to HOPS
nowhere dense	gray■	unknown to HOPS	unknown to HOPS
odd cycle transversal	gray■	unknown to HOPS	unknown to HOPS
outerplanar	gray■	unknown to HOPS	unknown to HOPS
overlap treewidth	gray■	unknown to HOPS	unknown to HOPS
path	cyan■	unknown to HOPS	exclusion
pathwidth	gray■	unknown to HOPS	unknown to HOPS
pathwidth+maxdegree	cyan■	unknown to HOPS	exclusion
perfect	gray■	unknown to HOPS	unknown to HOPS
planar	gray■	unknown to HOPS	unknown to HOPS
radius-inf flip-width	gray■	unknown to HOPS	unknown to HOPS
radius-r flip-width	gray■	unknown to HOPS	unknown to HOPS
rank-width	gray■	unknown to HOPS	unknown to HOPS
series-parallel	gray■	unknown to HOPS	unknown to HOPS
shrub-depth	gray■	unknown to HOPS	unknown to HOPS
sim-width	gray■	unknown to HOPS	unknown to HOPS
size	cyan■	unknown to HOPS	exclusion
slim tree-cut width	gray■	unknown to HOPS	unknown to HOPS
sparse twin-width	gray■	unknown to HOPS	unknown to HOPS
star	cyan■	unknown to HOPS	exclusion
stars	cyan■	unknown to HOPS	exclusion
strong coloring number	gray■	unknown to HOPS	unknown to HOPS
strong d-coloring number	gray■	unknown to HOPS	unknown to HOPS
strong inf-coloring number	gray■	unknown to HOPS	unknown to HOPS
topological bandwidth	gray■	unknown to HOPS	unknown to HOPS
tree	cyan■	unknown to HOPS	exclusion
tree-cut width	gray■	unknown to HOPS	unknown to HOPS
tree-independence number	gray■	unknown to HOPS	unknown to HOPS
tree-partition-width	gray■	unknown to HOPS	unknown to HOPS
treebandwidth	gray■	unknown to HOPS	unknown to HOPS
treedepth	gray■	unknown to HOPS	unknown to HOPS
treelength	gray■	unknown to HOPS	unknown to HOPS
treespan	cyan■	unknown to HOPS	exclusion
treewidth	gray■	unknown to HOPS	unknown to HOPS
twin-cover number	gray■	unknown to HOPS	unknown to HOPS
twin-width	gray■	unknown to HOPS	unknown to HOPS
vertex connectivity	yellow■	equal	equal
vertex cover	gray■	unknown to HOPS	unknown to HOPS
vertex integrity	gray■	unknown to HOPS	unknown to HOPS
weak coloring number	gray■	unknown to HOPS	unknown to HOPS
weak d-coloring number	gray■	unknown to HOPS	unknown to HOPS
weak inf-coloring number	gray■	unknown to HOPS	unknown to HOPS
weakly sparse	gray■	unknown to HOPS	unknown to HOPS
weakly sparse and merge width	gray■	unknown to HOPS	unknown to HOPS

Results

2022 Expanding the Graph Parameter Hierarchy by Tran
- page 34 : graph classes with bounded c-closure are not bounded vertex connectivity – Observation 5.7. $c$-Closure is incomparable to Distance to Disconnected, Domatic Number and Maximum Clique.
- page 34 : graph classes with bounded vertex connectivity are not bounded c-closure – Observation 5.7. $c$-Closure is incomparable to Distance to Disconnected, Domatic Number and Maximum Clique.
assumed
- vertex connectivity is equivalent to vertex connectivity – assumed