cycle

Definitions:

an intersetcion of connected, and cycles
Has a cyclic vertex order such that the graph contains edges for each pair of vertices that are next to each other in the order.
A connected graph with all vertices having degree two.

Relations

Other		Relation from	Relation to
acyclic chromatic number	red■	exclusion	upper bound
admissibility	red■	exclusion	upper bound
arboricity	red■	exclusion	upper bound
average degree	red■	exclusion	upper bound
average distance	magenta■	exclusion	unknown to HOPS
bandwidth	red■	exclusion	upper bound
bipartite	magenta■	exclusion	unknown to HOPS
bipartite number	magenta■	exclusion	unknown to HOPS
bisection bandwidth	red■	exclusion	upper bound
block	magenta■	exclusion	unknown to HOPS
book thickness	red■	exclusion	upper bound
boolean width	red■	exclusion	upper bound
bounded components	magenta■	exclusion	unknown to HOPS
bounded expansion	red■	exclusion	upper bound
boxicity	red■	exclusion	upper bound
branch width	red■	exclusion	upper bound
c-closure	red■	exclusion	upper bound
carving-width	red■	exclusion	upper bound
chi-bounded	red■	exclusion	upper bound
chordal	magenta■	exclusion	unknown to HOPS
chordality	red■	exclusion	upper bound
chromatic number	red■	exclusion	upper bound
clique cover number	magenta■	exclusion	unknown to HOPS
clique-tree-width	red■	exclusion	upper bound
clique-width	red■	exclusion	upper bound
cluster	magenta■	exclusion	unknown to HOPS
co-cluster	magenta■	exclusion	unknown to HOPS
cograph	magenta■	exclusion	unknown to HOPS
complete	magenta■	exclusion	unknown to HOPS
connected	red■	exclusion	upper bound
contraction complexity	red■	exclusion	upper bound
cutwidth	red■	exclusion	upper bound
cycle	yellow■	equal	equal
cycles	red■	exclusion	upper bound
d-admissibility	red■	exclusion	upper bound
d-path-free	magenta■	exclusion	unknown to HOPS
degeneracy	red■	exclusion	upper bound
degree treewidth	red■	exclusion	upper bound
diameter	magenta■	exclusion	unknown to HOPS
diameter+max degree	magenta■	exclusion	unknown to HOPS
distance to bipartite	red■	exclusion	upper bound
distance to block	red■	exclusion	upper bound
distance to bounded components	magenta■	exclusion	unknown to HOPS
distance to chordal	red■	exclusion	upper bound
distance to cluster	magenta■	exclusion	unknown to HOPS
distance to co-cluster	magenta■	exclusion	unknown to HOPS
distance to cograph	magenta■	exclusion	unknown to HOPS
distance to complete	magenta■	exclusion	unknown to HOPS
distance to edgeless	magenta■	exclusion	unknown to HOPS
distance to forest	red■	exclusion	upper bound
distance to interval	red■	exclusion	upper bound
distance to linear forest	red■	exclusion	upper bound
distance to maximum degree	red■	exclusion	upper bound
distance to outerplanar	red■	exclusion	upper bound
distance to perfect	red■	exclusion	upper bound
distance to planar	red■	exclusion	upper bound
distance to stars	magenta■	exclusion	unknown to HOPS
domatic number	red■	exclusion	upper bound
domination number	magenta■	exclusion	unknown to HOPS
domino treewidth	red■	exclusion	upper bound
edge clique cover number	magenta■	exclusion	unknown to HOPS
edge connectivity	red■	exclusion	upper bound
edge-cut width	red■	exclusion	upper bound
edge-treewidth	red■	exclusion	upper bound
edgeless	magenta■	exclusion	unknown to HOPS
excluded minor	red■	exclusion	upper bound
excluded planar minor	gray■	unknown to HOPS	unknown to HOPS
excluded top-minor	red■	exclusion	upper bound
feedback edge set	red■	exclusion	upper bound
feedback vertex set	red■	exclusion	upper bound
flip-width	red■	exclusion	upper bound
forest	magenta■	exclusion	unknown to HOPS
genus	red■	exclusion	upper bound
grid	magenta■	exclusion	unknown to HOPS
h-index	red■	exclusion	upper bound
interval	magenta■	exclusion	unknown to HOPS
iterated type partitions	magenta■	exclusion	unknown to HOPS
linear clique-width	red■	exclusion	upper bound
linear forest	magenta■	exclusion	unknown to HOPS
linear NLC-width	red■	exclusion	upper bound
linear rank-width	red■	exclusion	upper bound
maximum clique	red■	exclusion	upper bound
maximum degree	red■	exclusion	upper bound
maximum independent set	magenta■	exclusion	unknown to HOPS
maximum induced matching	magenta■	exclusion	unknown to HOPS
maximum leaf number	red■	exclusion	upper bound
maximum matching	magenta■	exclusion	unknown to HOPS
maximum matching on bipartite graphs	magenta■	exclusion	unknown to HOPS
merge-width	red■	exclusion	upper bound
mim-width	red■	exclusion	upper bound
minimum degree	red■	exclusion	upper bound
mm-width	red■	exclusion	upper bound
modular-width	magenta■	exclusion	unknown to HOPS
module-width	red■	exclusion	upper bound
monadically dependent	red■	exclusion	upper bound
monadically stable	red■	exclusion	upper bound
neighborhood diversity	magenta■	exclusion	unknown to HOPS
NLC-width	red■	exclusion	upper bound
NLCT-width	red■	exclusion	upper bound
nowhere dense	red■	exclusion	upper bound
odd cycle transversal	red■	exclusion	upper bound
outerplanar	gray■	unknown to HOPS	unknown to HOPS
overlap treewidth	red■	exclusion	upper bound
path	gray■	unknown to HOPS	unknown to HOPS
pathwidth	red■	exclusion	upper bound
pathwidth+maxdegree	red■	exclusion	upper bound
perfect	magenta■	exclusion	unknown to HOPS
planar	magenta■	exclusion	unknown to HOPS
radius-inf flip-width	red■	exclusion	upper bound
radius-r flip-width	red■	exclusion	upper bound
rank-width	red■	exclusion	upper bound
series-parallel	gray■	unknown to HOPS	unknown to HOPS
shrub-depth	magenta■	exclusion	unknown to HOPS
sim-width	red■	exclusion	upper bound
size	magenta■	exclusion	unknown to HOPS
slim tree-cut width	red■	exclusion	upper bound
sparse twin-width	red■	exclusion	upper bound
star	magenta■	exclusion	unknown to HOPS
stars	magenta■	exclusion	unknown to HOPS
strong coloring number	red■	exclusion	upper bound
strong d-coloring number	red■	exclusion	upper bound
strong inf-coloring number	red■	exclusion	upper bound
topological bandwidth	red■	exclusion	upper bound
tree	magenta■	exclusion	unknown to HOPS
tree-cut width	red■	exclusion	upper bound
tree-independence number	red■	exclusion	upper bound
tree-partition-width	red■	exclusion	upper bound
treebandwidth	red■	exclusion	upper bound
treedepth	magenta■	exclusion	unknown to HOPS
treelength	magenta■	exclusion	unknown to HOPS
treespan	red■	exclusion	upper bound
treewidth	red■	exclusion	upper bound
twin-cover number	magenta■	exclusion	unknown to HOPS
twin-width	red■	exclusion	upper bound
vertex connectivity	magenta■	exclusion	unknown to HOPS
vertex cover	magenta■	exclusion	unknown to HOPS
vertex integrity	magenta■	exclusion	unknown to HOPS
weak coloring number	red■	exclusion	upper bound
weak d-coloring number	red■	exclusion	upper bound
weak inf-coloring number	magenta■	exclusion	unknown to HOPS
weakly sparse	red■	exclusion	upper bound
weakly sparse and merge width	red■	exclusion	upper bound

Results

unknown source
- cycle upper bounds maximum leaf number by a constant
assumed
- cycle upper bounds connected by a constant – by definition
- cycle upper bounds cycles by a constant – by definition
- cycle is equivalent to cycle – assumed