average degree
equivalent to: average degree
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | upper bound | exclusion |
arboricity | upper bound | exclusion |
average distance | exclusion | exclusion |
bandwidth | upper bound | exclusion |
bipartite | unbounded | exclusion |
bipartite number | exclusion | unknown to HOPS |
bisection bandwidth | exclusion | exclusion |
block | unbounded | exclusion |
book thickness | upper bound | exclusion |
boolean width | exclusion | exclusion |
bounded components | upper bound | exclusion |
boxicity | exclusion | exclusion |
branch width | upper bound | exclusion |
c-closure | exclusion | exclusion |
carving-width | upper bound | exclusion |
chordal | unbounded | exclusion |
chordality | exclusion | exclusion |
chromatic number | exclusion | exclusion |
clique cover number | exclusion | exclusion |
clique-tree-width | exclusion | exclusion |
clique-width | exclusion | exclusion |
cluster | unbounded | exclusion |
co-cluster | unbounded | exclusion |
cograph | unbounded | exclusion |
complete | unbounded | exclusion |
connected | unbounded | unknown to HOPS |
cutwidth | upper bound | exclusion |
cycle | constant | exclusion |
cycles | constant | exclusion |
d-path-free | upper bound | exclusion |
degeneracy | upper bound | exclusion |
degree treewidth | upper bound | exclusion |
diameter | exclusion | exclusion |
diameter+max degree | upper bound | exclusion |
disjoint cycles | constant | 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 | exclusion | exclusion |
distance to co-cluster | exclusion | exclusion |
distance to cograph | exclusion | exclusion |
distance to complete | exclusion | exclusion |
distance to edgeless | upper bound | exclusion |
distance to forest | upper bound | exclusion |
distance to interval | exclusion | exclusion |
distance to linear forest | upper bound | exclusion |
distance to maximum degree | upper bound | exclusion |
distance to outerplanar | upper bound | exclusion |
distance to perfect | exclusion | exclusion |
distance to planar | unknown to HOPS | exclusion |
distance to stars | upper bound | exclusion |
domatic number | unknown to HOPS | upper bound |
domination number | exclusion | exclusion |
edge clique cover number | exclusion | exclusion |
edge connectivity | exclusion | upper bound |
edgeless | constant | exclusion |
feedback edge set | upper bound | exclusion |
feedback vertex set | upper bound | exclusion |
forest | constant | exclusion |
genus | upper bound | exclusion |
girth | exclusion | exclusion |
grid | constant | exclusion |
h-index | upper bound | exclusion |
inf-flip-width | exclusion | exclusion |
interval | unbounded | exclusion |
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 | upper bound | 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 | unknown to HOPS | upper bound |
mm-width | upper bound | 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 | constant | exclusion |
path | constant | exclusion |
pathwidth | upper bound | exclusion |
pathwidth+maxdegree | upper bound | exclusion |
perfect | unbounded | exclusion |
planar | constant | 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 | upper bound | exclusion |
tree | constant | exclusion |
tree-independence number | unknown to HOPS | unknown to HOPS |
treedepth | upper bound | exclusion |
treelength | exclusion | unknown to HOPS |
treewidth | upper bound | exclusion |
twin-cover number | exclusion | exclusion |
twin-width | exclusion | exclusion |
vertex connectivity | unknown to HOPS | unknown to HOPS |
vertex cover | upper bound | exclusion |
vertex integrity | upper bound | exclusion |
Results
- 2019 The Graph Parameter Hierarchy by Sorge
- page 3 : average degree – The \emph{average degree} of a graph $G = (V,E)$ is $2|E|/|V|$.
- Comparing Graph Parameters by Schröder
- page 35 : bounded average degree does not imply bounded maximum clique – Proposition 3.35
- page 36 : bounded average degree does not imply bounded chordality – Proposition 3.36
- https://bookdown.org/omarlizardo/_main/2-7-average-degree.html
- average degree – Average degree is simply the average number of edges per node in the graph. … Total Edges/Total Nodes=Average Degree
- assumed
- average degree upper bounds minimum degree by a linear function – By definition
- https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.3190120309
- average degree – The average distance in a graph is defined as the average length of a shortest path between two vertices, taken over all pairs of vertices.
- unknown source
- degeneracy upper bounds average degree by a linear function – Removing a vertex of degree $d$ increases the value added to the sum of all degrees by at most $2d$, hence, the average is no more than twice the degeneracy.