maximum leaf number

providers: ISGCI

Relations

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

Results

2019 The Graph Parameter Hierarchy by Sorge
- page 8 : maximum leaf number upper bounds distance to linear forest by a linear function – Lemma 4.10 ([14]). The max-leaf number $\mathrm{ml}$ upper bounds the distance to disjoint paths $d$. We have $d \le \mathrm{ml}-1$.
- page 10 : maximum leaf number upper bounds bandwidth by a linear function – Lemma 4.25. The max leaf number $\mathrm{ml}$ strictly upper bounds the bandwidth $\mathrm{bw}$.
Comparing Graph Parameters by Schröder
- page 21 : bounded maximum leaf number does not imply bounded girth – Proposition 3.14
https://mathworld.wolfram.com/MaximumLeafNumber.html
- maximum leaf number – … the largest number of tree leaves in any of its spanning trees.
unknown source
- maximum leaf number upper bounds distance to linear forest by a computable function
- maximum leaf number upper bounds feedback edge set by a computable function
- graph class cycle has constant maximum leaf number
- maximum leaf number upper bounds feedback edge set by a polynomial function – M. Bentert (personal communication)