diameter
equivalent to: diameter
providers: ISGCI
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | exclusion | exclusion |
arboricity | exclusion | exclusion |
average degree | exclusion | exclusion |
average distance | unknown to HOPS | upper bound |
bandwidth | exclusion | exclusion |
bipartite | unbounded | exclusion |
bipartite number | unknown to HOPS | upper bound |
bisection bandwidth | exclusion | exclusion |
block | unbounded | exclusion |
book thickness | exclusion | exclusion |
boolean width | exclusion | exclusion |
bounded components | upper bound | exclusion |
boxicity | exclusion | exclusion |
branch width | exclusion | exclusion |
c-closure | exclusion | exclusion |
carving-width | exclusion | exclusion |
chordal | unbounded | exclusion |
chordality | exclusion | exclusion |
chromatic number | exclusion | exclusion |
clique cover number | upper bound | exclusion |
clique-tree-width | exclusion | exclusion |
clique-width | exclusion | exclusion |
cluster | constant | exclusion |
co-cluster | constant | exclusion |
cograph | constant | exclusion |
complete | constant | exclusion |
connected | unbounded | unknown to HOPS |
cutwidth | exclusion | exclusion |
cycle | unbounded | exclusion |
cycles | unbounded | exclusion |
d-path-free | upper bound | exclusion |
degeneracy | exclusion | exclusion |
degree treewidth | exclusion | exclusion |
diameter+max degree | upper bound | exclusion |
disjoint cycles | unbounded | exclusion |
distance to bipartite | exclusion | exclusion |
distance to block | exclusion | exclusion |
distance to bounded components | upper bound | exclusion |
distance to chordal | exclusion | exclusion |
distance to cluster | unknown to HOPS | exclusion |
distance to co-cluster | upper bound | exclusion |
distance to cograph | upper bound | exclusion |
distance to complete | upper bound | exclusion |
distance to edgeless | upper bound | exclusion |
distance to forest | exclusion | exclusion |
distance to interval | exclusion | exclusion |
distance to linear forest | exclusion | exclusion |
distance to maximum degree | exclusion | exclusion |
distance to outerplanar | exclusion | exclusion |
distance to perfect | exclusion | exclusion |
distance to planar | exclusion | exclusion |
distance to stars | upper bound | exclusion |
domatic number | exclusion | exclusion |
domination number | upper bound | exclusion |
edge clique cover number | upper bound | exclusion |
edge connectivity | exclusion | exclusion |
edgeless | constant | exclusion |
feedback edge set | exclusion | exclusion |
feedback vertex set | exclusion | exclusion |
forest | unbounded | exclusion |
genus | exclusion | exclusion |
girth | unknown to HOPS | upper bound |
grid | unbounded | exclusion |
h-index | exclusion | exclusion |
inf-flip-width | exclusion | exclusion |
interval | unbounded | exclusion |
iterated type partitions | upper bound | exclusion |
linear clique-width | exclusion | exclusion |
linear forest | unbounded | exclusion |
linear NLC-width | exclusion | exclusion |
linear rank-width | exclusion | exclusion |
maximum clique | exclusion | exclusion |
maximum degree | exclusion | exclusion |
maximum independent set | upper bound | exclusion |
maximum induced matching | upper bound | unknown to HOPS |
maximum leaf number | exclusion | exclusion |
maximum matching | upper bound | exclusion |
maximum matching on bipartite graphs | upper bound | exclusion |
mim-width | exclusion | unknown to HOPS |
minimum degree | exclusion | exclusion |
mm-width | exclusion | exclusion |
modular-width | upper bound | exclusion |
module-width | exclusion | exclusion |
neighborhood diversity | upper bound | exclusion |
NLC-width | exclusion | exclusion |
NLCT-width | exclusion | exclusion |
odd cycle transversal | exclusion | exclusion |
outerplanar | unbounded | exclusion |
path | unbounded | exclusion |
pathwidth | exclusion | exclusion |
pathwidth+maxdegree | exclusion | exclusion |
perfect | unbounded | exclusion |
planar | unbounded | exclusion |
radius-r flip-width | exclusion | unknown to HOPS |
rank-width | exclusion | exclusion |
shrub-depth | unknown to HOPS | exclusion |
sim-width | exclusion | unknown to HOPS |
star | constant | exclusion |
stars | constant | exclusion |
topological bandwidth | exclusion | exclusion |
tree | unbounded | exclusion |
tree-independence number | exclusion | unknown to HOPS |
treedepth | upper bound | exclusion |
treelength | unknown to HOPS | upper bound |
treewidth | exclusion | exclusion |
twin-cover number | upper bound | exclusion |
twin-width | exclusion | exclusion |
vertex connectivity | unknown to HOPS | exclusion |
vertex cover | upper bound | exclusion |
vertex integrity | upper bound | exclusion |
Results
- 2022 Expanding the Graph Parameter Hierarchy by Tran
- page 25 : modular-width upper bounds diameter by a linear function – Theorem 4.7. Modular-width strictly upper bounds Max Diameter of Components.
- page 25 : bounded diameter does not imply bounded modular-width – Theorem 4.7. Modular-width strictly upper bounds Max Diameter of Components.
- Comparing Graph Parameters by Schröder
- https://en.wikipedia.org/wiki/Distance_(graph_theory)#Related_concepts
- diameter – … [diameter] is the greatest distance between any pair of vertices …
- assumed
- diameter upper bounds average distance by a linear function – By definition
- diameter upper bounds treelength by a linear function – By definition
- diameter+max degree upper bounds diameter by a linear function – by definition
- unknown source
- domination number upper bounds diameter by a linear function – An unbounded diameter implies a long path where no vertices that are more than $3$ apart may be dominated by the same dominating vertex, otherwise we could shorten the path. Hence, the number of dominating vertices is also unbounded.
- distance to cograph upper bounds diameter by a linear function
- maximum induced matching upper bounds diameter by a linear function – Diameter requires an induced path on $d$ edges, hence, maximum induced matching is at least $\lfloor (d+1)/3 \rfloor$.
- modular-width upper bounds diameter by a computable function
- diameter – Maximum distance of two vertices that are in the same connected component.
- graph class path has unbounded diameter – trivially