edgeless
equivalent to: edgeless
providers: ISGCI
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | exclusion | constant |
arboricity | exclusion | constant |
average degree | exclusion | constant |
average distance | exclusion | constant |
bandwidth | exclusion | unknown to HOPS |
bipartite | exclusion | inclusion |
bipartite number | exclusion | constant |
bisection bandwidth | exclusion | constant |
block | exclusion | inclusion |
book thickness | exclusion | constant |
boolean width | exclusion | constant |
bounded components | exclusion | constant |
boxicity | exclusion | constant |
branch width | exclusion | constant |
c-closure | exclusion | constant |
carving-width | exclusion | constant |
chordal | exclusion | inclusion |
chordality | exclusion | constant |
chromatic number | exclusion | constant |
clique cover number | exclusion | unbounded |
clique-tree-width | exclusion | constant |
clique-width | exclusion | constant |
cluster | exclusion | inclusion |
co-cluster | exclusion | inclusion |
cograph | exclusion | inclusion |
complete | exclusion | exclusion |
connected | exclusion | unknown to HOPS |
cutwidth | exclusion | constant |
cycle | exclusion | unknown to HOPS |
cycles | exclusion | unknown to HOPS |
d-path-free | exclusion | constant |
degeneracy | exclusion | constant |
degree treewidth | exclusion | constant |
diameter | exclusion | constant |
diameter+max degree | exclusion | constant |
disjoint cycles | exclusion | inclusion |
distance to bipartite | exclusion | constant |
distance to block | exclusion | constant |
distance to bounded components | exclusion | constant |
distance to chordal | exclusion | constant |
distance to cluster | exclusion | constant |
distance to co-cluster | exclusion | constant |
distance to cograph | exclusion | constant |
distance to complete | exclusion | unbounded |
distance to edgeless | exclusion | constant |
distance to forest | exclusion | constant |
distance to interval | exclusion | constant |
distance to linear forest | exclusion | constant |
distance to maximum degree | exclusion | constant |
distance to outerplanar | exclusion | constant |
distance to perfect | exclusion | constant |
distance to planar | exclusion | constant |
distance to stars | exclusion | constant |
domatic number | exclusion | constant |
domination number | exclusion | unbounded |
edge clique cover number | exclusion | unknown to HOPS |
edge connectivity | exclusion | constant |
feedback edge set | exclusion | constant |
feedback vertex set | exclusion | constant |
forest | exclusion | inclusion |
genus | exclusion | constant |
girth | exclusion | constant |
grid | exclusion | unknown to HOPS |
h-index | exclusion | constant |
inf-flip-width | exclusion | constant |
interval | exclusion | inclusion |
iterated type partitions | exclusion | constant |
linear clique-width | exclusion | constant |
linear forest | exclusion | inclusion |
linear NLC-width | exclusion | constant |
linear rank-width | exclusion | constant |
maximum clique | exclusion | constant |
maximum degree | exclusion | constant |
maximum independent set | exclusion | unbounded |
maximum induced matching | exclusion | constant |
maximum leaf number | exclusion | unknown to HOPS |
maximum matching | exclusion | constant |
maximum matching on bipartite graphs | exclusion | constant |
mim-width | exclusion | constant |
minimum degree | exclusion | constant |
mm-width | exclusion | constant |
modular-width | exclusion | constant |
module-width | exclusion | constant |
neighborhood diversity | exclusion | constant |
NLC-width | exclusion | constant |
NLCT-width | exclusion | constant |
odd cycle transversal | exclusion | constant |
outerplanar | exclusion | inclusion |
path | exclusion | unknown to HOPS |
pathwidth | exclusion | constant |
pathwidth+maxdegree | exclusion | constant |
perfect | exclusion | inclusion |
planar | exclusion | inclusion |
radius-r flip-width | exclusion | constant |
rank-width | exclusion | constant |
shrub-depth | exclusion | constant |
sim-width | exclusion | constant |
star | exclusion | unknown to HOPS |
stars | exclusion | inclusion |
topological bandwidth | exclusion | unknown to HOPS |
tree | exclusion | unknown to HOPS |
tree-independence number | exclusion | constant |
treedepth | exclusion | constant |
treelength | exclusion | constant |
treewidth | exclusion | constant |
twin-cover number | exclusion | constant |
twin-width | exclusion | constant |
vertex connectivity | exclusion | unknown to HOPS |
vertex cover | exclusion | constant |
vertex integrity | exclusion | constant |
Results
- 2017 Graph Theory by Diestel
- page 5 : edgeless – A vertex of degree $0$ is \emph{isolated}.
- assumed
- graph class edgeless is included in graph class linear forest
- graph class linear forest is not included in graph class edgeless
- graph class edgeless is included in graph class stars
- graph class stars is not included in graph class edgeless
- graph class edgeless is included in graph class co-cluster
- graph class co-cluster is not included in graph class edgeless
- graph class edgeless is included in graph class cluster
- graph class cluster is not included in graph class edgeless
- graph class edgeless has constant distance to edgeless – by definition
- graph class edgeless has constant bounded components – By definition
- unknown source
- graph class edgeless has constant vertex cover
- graph class edgeless has unbounded domination number
- graph class edgeless has constant maximum matching