chordal

equivalent to: chordal

providers: ISGCI

Relations

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

Results

2017 Graph Theory by Diestel
- page 135 : chordal – … a graph is chordal (or triangulated) if each of its cycles of length at least $4$ has a chord, i.e. if it contains no induced cycles other than triangles.
assumed
- graph class chordal is included in graph class perfect
- graph class perfect is not included in graph class chordal
- graph class interval is included in graph class chordal
- graph class chordal is not included in graph class interval
- graph class block is included in graph class chordal
- graph class chordal is not included in graph class block
- graph class chordal has constant distance to chordal – by definition