tree-independence number

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

Results

unknown source
- treewidth upper bounds tree-independence number by a computable function
- tree-independence number upper bounds sim-width by a computable function
assumed
- tree-independence number is equivalent to tree-independence number – assumed