distance to cluster

providers: ISGCI

Relations

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

Results

2022 Expanding the Graph Parameter Hierarchy by Tran
- page 18 : twin-cover number upper bounds distance to cluster by a linear function – … graph $H$ with a twin cover of size $k$ has a distance to cluster of at most $k$.
- page 18 : bounded distance to cluster does not imply bounded twin-cover number – We show that twin cover number is not upper bounded by distance to cluster.
- page 28 : bounded modular-width does not imply bounded distance to cluster – Proposition 4.10. Modular-width is incomparable to Distance to Cluster.
- page 28 : bounded distance to cluster does not imply bounded modular-width – Proposition 4.10. Modular-width is incomparable to Distance to Cluster.
Comparing Graph Parameters by Schröder
- page 13 : bounded distance to cluster does not imply bounded distance to co-cluster – Proposition 3.3
assumed
- graph class cluster has constant distance to cluster – by definition
- twin-cover number upper bounds distance to cluster by a linear function – By definition
unknown source
- graph class path has unbounded distance to cluster – trivially