distance to interval
equivalent to: distance to interval
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | exclusion | exclusion |
arboricity | exclusion | exclusion |
average degree | exclusion | exclusion |
average distance | exclusion | exclusion |
bandwidth | exclusion | exclusion |
bipartite | unbounded | exclusion |
bipartite number | exclusion | unknown to HOPS |
bisection bandwidth | exclusion | exclusion |
block | unbounded | unknown to HOPS |
book thickness | exclusion | exclusion |
boolean width | exclusion | exclusion |
bounded components | exclusion | exclusion |
boxicity | exclusion | upper bound |
branch width | exclusion | exclusion |
c-closure | exclusion | exclusion |
carving-width | exclusion | exclusion |
chordal | unbounded | unknown to HOPS |
chordality | exclusion | upper bound |
chromatic number | exclusion | exclusion |
clique cover number | exclusion | exclusion |
clique-tree-width | exclusion | exclusion |
clique-width | exclusion | exclusion |
cluster | constant | exclusion |
co-cluster | unbounded | exclusion |
cograph | unbounded | exclusion |
complete | constant | exclusion |
connected | unbounded | unknown to HOPS |
cutwidth | exclusion | exclusion |
cycle | constant | exclusion |
cycles | unbounded | exclusion |
d-path-free | exclusion | exclusion |
degeneracy | exclusion | exclusion |
degree treewidth | exclusion | exclusion |
diameter | exclusion | exclusion |
diameter+max degree | exclusion | exclusion |
disjoint cycles | unbounded | exclusion |
distance to bipartite | exclusion | exclusion |
distance to block | exclusion | unknown to HOPS |
distance to bounded components | exclusion | exclusion |
distance to chordal | exclusion | upper bound |
distance to cluster | upper bound | exclusion |
distance to co-cluster | exclusion | exclusion |
distance to cograph | exclusion | exclusion |
distance to complete | upper bound | exclusion |
distance to edgeless | upper bound | exclusion |
distance to forest | exclusion | exclusion |
distance to linear forest | upper bound | exclusion |
distance to maximum degree | exclusion | exclusion |
distance to outerplanar | exclusion | exclusion |
distance to perfect | exclusion | upper bound |
distance to planar | exclusion | exclusion |
distance to stars | upper bound | exclusion |
domatic number | exclusion | exclusion |
domination number | exclusion | exclusion |
edge clique cover number | exclusion | 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 | exclusion | exclusion |
grid | unbounded | exclusion |
h-index | exclusion | exclusion |
inf-flip-width | exclusion | exclusion |
interval | constant | unknown to HOPS |
iterated type partitions | exclusion | exclusion |
linear clique-width | exclusion | exclusion |
linear forest | constant | exclusion |
linear NLC-width | exclusion | exclusion |
linear rank-width | exclusion | exclusion |
maximum clique | exclusion | exclusion |
maximum degree | exclusion | exclusion |
maximum independent set | exclusion | exclusion |
maximum induced matching | exclusion | exclusion |
maximum leaf number | upper bound | exclusion |
maximum matching | unknown to HOPS | 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 | exclusion | exclusion |
module-width | exclusion | exclusion |
neighborhood diversity | exclusion | exclusion |
NLC-width | exclusion | exclusion |
NLCT-width | exclusion | exclusion |
odd cycle transversal | exclusion | exclusion |
outerplanar | unbounded | exclusion |
path | constant | exclusion |
pathwidth | exclusion | exclusion |
pathwidth+maxdegree | exclusion | exclusion |
perfect | unbounded | unknown to HOPS |
planar | unbounded | exclusion |
radius-r flip-width | exclusion | unknown to HOPS |
rank-width | exclusion | exclusion |
shrub-depth | exclusion | exclusion |
sim-width | exclusion | unknown to HOPS |
star | constant | exclusion |
stars | constant | exclusion |
topological bandwidth | exclusion | exclusion |
tree | unknown to HOPS | exclusion |
tree-independence number | exclusion | unknown to HOPS |
treedepth | exclusion | exclusion |
treelength | exclusion | unknown to HOPS |
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 | exclusion | exclusion |
Results
- 2022 Expanding the Graph Parameter Hierarchy by Tran
- page 38 : bounded twin-width does not imply bounded distance to interval – Observation 6.5. Twin-width is incomparable to Distance to Interval.
- page 38 : bounded distance to interval does not imply bounded twin-width – Observation 6.5. Twin-width is incomparable to Distance to Interval.
- 2019 The Graph Parameter Hierarchy by Sorge
- page 9 : distance to interval upper bounds boxicity by a linear function – Lemma 4.16. The distance $i$ to an interval graph upper bounds the boxicity $b$. We have $b \le i+1$.
- unknown source
- graph class forest has unbounded distance to interval
- assumed
- graph class interval has constant distance to interval – by definition
- distance to interval upper bounds boxicity by a linear function – By definition
- Comparing Graph Parameters by Schröder
- page 25 : bounded feedback edge set does not imply bounded distance to interval – Proposition 3.21