topological bandwidth
tags: vertex order
equivalent to: topological bandwidth
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 | upper bound | unknown to HOPS |
bipartite | unbounded | exclusion |
bipartite number | exclusion | unknown to HOPS |
bisection bandwidth | exclusion | upper bound |
block | unbounded | exclusion |
book thickness | exclusion | upper bound |
boolean width | exclusion | upper bound |
bounded components | unknown to HOPS | exclusion |
boxicity | exclusion | upper bound |
branch width | exclusion | upper bound |
c-closure | exclusion | unknown to HOPS |
carving-width | unknown to HOPS | unknown to HOPS |
chordal | unbounded | exclusion |
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 | unknown to HOPS | unknown to HOPS |
cycle | constant | exclusion |
cycles | unknown to HOPS | exclusion |
d-path-free | exclusion | exclusion |
degeneracy | exclusion | upper bound |
degree treewidth | unknown to HOPS | unknown to HOPS |
diameter | exclusion | exclusion |
diameter+max degree | unknown to HOPS | exclusion |
disjoint cycles | unbounded | exclusion |
distance to bipartite | exclusion | exclusion |
distance to block | exclusion | exclusion |
distance to bounded components | exclusion | exclusion |
distance to chordal | exclusion | exclusion |
distance to cluster | exclusion | exclusion |
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 | exclusion |
distance to interval | exclusion | exclusion |
distance to linear forest | exclusion | exclusion |
distance to maximum degree | exclusion | unknown to HOPS |
distance to outerplanar | exclusion | exclusion |
distance to perfect | exclusion | exclusion |
distance to planar | exclusion | exclusion |
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 | exclusion |
feedback vertex set | exclusion | exclusion |
forest | unbounded | exclusion |
genus | exclusion | exclusion |
girth | exclusion | exclusion |
grid | unbounded | exclusion |
h-index | exclusion | unknown to HOPS |
inf-flip-width | exclusion | upper bound |
interval | unbounded | exclusion |
iterated type partitions | exclusion | exclusion |
linear clique-width | exclusion | upper bound |
linear forest | unknown to HOPS | exclusion |
linear NLC-width | exclusion | upper bound |
linear rank-width | exclusion | upper bound |
maximum clique | exclusion | upper bound |
maximum degree | exclusion | unknown to HOPS |
maximum independent set | exclusion | exclusion |
maximum induced matching | exclusion | exclusion |
maximum leaf number | upper bound | exclusion |
maximum matching | exclusion | exclusion |
maximum matching on bipartite graphs | unknown to HOPS | 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 | exclusion |
outerplanar | unbounded | exclusion |
path | unknown to HOPS | exclusion |
pathwidth | exclusion | upper bound |
pathwidth+maxdegree | unknown to HOPS | unknown to HOPS |
perfect | unbounded | exclusion |
planar | unbounded | exclusion |
radius-r flip-width | exclusion | upper bound |
rank-width | exclusion | upper bound |
shrub-depth | exclusion | unknown to HOPS |
sim-width | exclusion | upper bound |
star | unknown to HOPS | exclusion |
stars | unknown to HOPS | exclusion |
tree | unbounded | exclusion |
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 | unknown to HOPS | unknown to HOPS |
vertex cover | exclusion | exclusion |
vertex integrity | exclusion | exclusion |
Results
- 2013 The Power of Data Reduction: Kernels for Fundamental Graph Problems by Jansen
- topological bandwidth – The \emph{topological bandwidth} of a graph $G$ is the minimum bandwidth over all subdivisions of $G$
- 1998 A partial $k$-arboretum of graphs with bounded treewidth by Bodlaender
- page 22 : topological bandwidth – The \emph{topological bandwidth} of a graph $G$ is the minimum bandwidth over all graphs $G’$ which are obtained by addition of an arbitrary number of vertices along edges of $G$.
- page 23 : topological bandwidth upper bounds pathwidth by a linear function – Theorem 45. For every graph $G$, the pathwidth of $G$ is at most the topological band-width of $G$.
- assumed
- bandwidth upper bounds topological bandwidth by a linear function – By definition
- 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.