distance to chordal

Relations

Other	Relation from	Relation to
acyclic chromatic number	exclusion	exclusion
arboricity	exclusion	exclusion
average degree	exclusion	exclusion
average distance	exclusion	exclusion
bandwidth	exclusion	exclusion
bipartite	unbounded	exclusion
bipartite number	exclusion	unknown to HOPS
bisection bandwidth	exclusion	exclusion
block	constant	exclusion
book thickness	exclusion	exclusion
boolean width	exclusion	exclusion
bounded components	exclusion	exclusion
boxicity	exclusion	exclusion
branch width	exclusion	exclusion
c-closure	exclusion	exclusion
carving-width	exclusion	exclusion
chordal	constant	unknown to HOPS
chordality	exclusion	upper bound
chromatic number	exclusion	exclusion
clique cover number	exclusion	exclusion
clique-tree-width	exclusion	exclusion
clique-width	exclusion	exclusion
cluster	constant	exclusion
co-cluster	unbounded	exclusion
cograph	unbounded	exclusion
complete	constant	exclusion
connected	unbounded	unknown to HOPS
cutwidth	exclusion	exclusion
cycle	constant	exclusion
cycles	unbounded	exclusion
d-path-free	exclusion	exclusion
degeneracy	exclusion	exclusion
degree treewidth	exclusion	exclusion
diameter	exclusion	exclusion
diameter+max degree	exclusion	exclusion
disjoint cycles	unbounded	exclusion
distance to bipartite	exclusion	exclusion
distance to block	upper bound	unknown to HOPS
distance to bounded components	exclusion	exclusion
distance to cluster	upper bound	exclusion
distance to co-cluster	exclusion	exclusion
distance to cograph	exclusion	exclusion
distance to complete	upper bound	exclusion
distance to edgeless	upper bound	exclusion
distance to forest	upper bound	exclusion
distance to interval	upper bound	exclusion
distance to linear forest	upper bound	exclusion
distance to maximum degree	exclusion	exclusion
distance to outerplanar	exclusion	exclusion
distance to perfect	exclusion	upper bound
distance to planar	exclusion	exclusion
distance to stars	upper bound	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	upper bound	exclusion
feedback vertex set	upper bound	exclusion
forest	constant	exclusion
genus	exclusion	exclusion
girth	exclusion	exclusion
grid	unbounded	exclusion
h-index	exclusion	exclusion
inf-flip-width	exclusion	exclusion
interval	constant	exclusion
iterated type partitions	exclusion	exclusion
linear clique-width	exclusion	exclusion
linear forest	constant	exclusion
linear NLC-width	exclusion	exclusion
linear rank-width	exclusion	exclusion
maximum clique	exclusion	exclusion
maximum degree	exclusion	exclusion
maximum independent set	exclusion	exclusion
maximum induced matching	exclusion	exclusion
maximum leaf number	upper bound	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	exclusion
neighborhood diversity	exclusion	exclusion
NLC-width	exclusion	exclusion
NLCT-width	exclusion	exclusion
odd cycle transversal	exclusion	exclusion
outerplanar	unbounded	exclusion
path	constant	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	exclusion
shrub-depth	exclusion	exclusion
sim-width	exclusion	unknown to HOPS
star	constant	exclusion
stars	constant	exclusion
topological bandwidth	exclusion	exclusion
tree	constant	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	exclusion
vertex connectivity	unknown to HOPS	exclusion
vertex cover	upper bound	exclusion
vertex integrity	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 $c \le f$.
unknown source
- graph class co-cluster has unbounded distance to chordal
- graph class grid has unbounded distance to chordal
assumed
- graph class chordal has constant distance to chordal – by definition
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