edge connectivity
equivalent to: edge connectivity
Relations
| Other | Relation from | Relation to |
|---|---|---|
| acyclic chromatic number | upper bound | exclusion |
| arboricity | upper bound | exclusion |
| average degree | upper bound | exclusion |
| average distance | exclusion | exclusion |
| bandwidth | upper bound | exclusion |
| bipartite | unbounded | exclusion |
| bipartite number | exclusion | unknown to HOPS |
| bisection bandwidth | upper bound | 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 | unknown to HOPS | 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 | exclusion |
| domination number | exclusion | exclusion |
| edge clique cover number | exclusion | exclusion |
| 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 | upper bound | exclusion |
| 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
- 2022 Expanding the Graph Parameter Hierarchy by Tran
- page 19 : bounded twin-cover number does not imply bounded edge connectivity – Observation 3.4. Twin Cover Number is incomparable to Maximum Clique, Domatic Number and Distance to Disconnected.
- page 19 : bounded edge connectivity does not imply bounded twin-cover number – Observation 3.4. Twin Cover Number is incomparable to Maximum Clique, Domatic Number and Distance to Disconnected.
- assumed
- bisection bandwidth upper bounds edge connectivity by a linear function – By definition
- https://mathworld.wolfram.com/EdgeConnectivity.html
- edge connectivity – The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges $\lambda(G)$ whose deletion from a graph $G$ disconnects $G$.
- unknown source
- minimum degree upper bounds edge connectivity by a linear function – Removing edges incident to the minimum degree vertex disconnects the graph.
- graph class complete has unbounded edge connectivity – Parameter is unbounded for the graph class of cliques.
- graph class bipartite has unbounded edge connectivity