distance to chordal

Relations

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

Results

2019 The Graph Parameter Hierarchy by Sorge
- page 9 : distance to chordal upper bounds chordality by a linear function – (ed: apparently goes as the lemma for ddist to interval and boxicity) Lemma 4.16. The distance $i$ to an interval graph upper bounds the boxicity $b$. We have $b \le i+1$.
- page 10 : feedback vertex set upper bounds distance to chordal by a linear function – Lemma 4.20. The feedback edge set number $f$ upper bounds the distance to a chordal graph $c$. We have $c \le f$.
assumed
- chordal upper bounds distance to chordal by a constant – by definition
- distance to chordal is equivalent to distance to chordal – assumed
Comparing Graph Parameters by Schröder
- page 20 : bounded distance to co-cluster does not imply bounded distance to chordal – Proposition 3.12
- page 20 : bounded distance to bipartite does not imply bounded distance to chordal – Proposition 3.12
- page 27 : bounded distance to chordal does not imply bounded boxicity – Proposition 3.25
unknown source
- graph class co-cluster has unbounded distance to chordal
- graph class grid has unbounded distance to chordal