bisection bandwidth

Relations

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

Results

2022 Expanding the Graph Parameter Hierarchy by Tran
- page 34 : bounded c-closure does not imply bounded bisection bandwidth – Proposition 5.5. $c$-Closure is incomparable to Bisection Width.
- page 34 : bounded bisection bandwidth does not imply bounded c-closure – Proposition 5.5. $c$-Closure is incomparable to Bisection Width.
- page 40 : bounded twin-width does not imply bounded bisection bandwidth – Observation 6.9. Twin-width is incomparable to Bisection Width.
- page 40 : bounded bisection bandwidth does not imply bounded twin-width – Observation 6.9. Twin-width is incomparable to Bisection Width.
assumed
- bisection bandwidth upper bounds edge connectivity by a linear function – By definition
- bisection bandwidth is equivalent to bisection bandwidth – assumed
unknown source
- topological bandwidth upper bounds bisection bandwidth by a linear function – Order vertices by their bandwidth integer. We split the graph in the middle of this ordering. There are at most roughly $k^2/2$ edges over this split.
- graph class grid has unbounded bisection bandwidth
- disjoint cycles upper bounds bisection bandwidth by a constant
- outerplanar upper bounds bisection bandwidth by a constant
- bisection bandwidth upper bounds distance to disconnected by a computable function
Comparing Graph Parameters by Schröder
- page 24 : bounded vertex cover does not imply bounded bisection bandwidth – Proposition 3.20
- page 28 : bounded maximum degree does not imply bounded bisection bandwidth – Proposition 3.26
- page 28 : bounded distance to bipartite does not imply bounded bisection bandwidth – Proposition 3.26
- page 30 : bounded bisection bandwidth does not imply bounded domatic number – Proposition 3.28
- page 30 : bounded feedback edge set does not imply bounded bisection bandwidth – Proposition 3.29
- page 33 : bounded bisection bandwidth does not imply bounded chordality – Proposition 3.31
- page 33 : bounded bisection bandwidth does not imply bounded clique-width – Proposition 3.32
- page 33 : bounded bisection bandwidth does not imply bounded maximum clique – Proposition 3.33