cycle

equivalent to: cycle

Relations

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

Results

assumed
- graph class cycle is included in graph class connected – by definition
- graph class cycle is included in graph class cycles – by definition
unknown source
- graph class cycle has constant maximum leaf number
- graph class cycle has unbounded girth