vertex connectivity
equivalent to: vertex connectivity
Relations
| Other | Relation from | Relation to |
|---|---|---|
| acyclic chromatic number | unknown to HOPS | unknown to HOPS |
| arboricity | unknown to HOPS | unknown to HOPS |
| average degree | unknown to HOPS | unknown to HOPS |
| average distance | exclusion | unknown to HOPS |
| bandwidth | unknown to HOPS | exclusion |
| bipartite | unknown to HOPS | unknown to HOPS |
| bipartite number | exclusion | unknown to HOPS |
| bisection bandwidth | unknown to HOPS | unknown to HOPS |
| block | unknown to HOPS | unknown to HOPS |
| book thickness | unknown to HOPS | unknown to HOPS |
| boolean width | exclusion | unknown to HOPS |
| bounded components | unknown to HOPS | exclusion |
| boxicity | exclusion | unknown to HOPS |
| branch width | unknown to HOPS | unknown to HOPS |
| c-closure | exclusion | exclusion |
| carving-width | unknown to HOPS | exclusion |
| chordal | unknown to HOPS | unknown to HOPS |
| chordality | exclusion | unknown to HOPS |
| chromatic number | exclusion | unknown to HOPS |
| clique cover number | exclusion | unknown to HOPS |
| clique-tree-width | exclusion | unknown to HOPS |
| clique-width | exclusion | unknown to HOPS |
| cluster | unknown to HOPS | unknown to HOPS |
| co-cluster | unknown to HOPS | unknown to HOPS |
| cograph | unknown to HOPS | unknown to HOPS |
| complete | unknown to HOPS | unknown to HOPS |
| connected | unknown to HOPS | unknown to HOPS |
| cutwidth | unknown to HOPS | exclusion |
| cycle | unknown to HOPS | exclusion |
| cycles | unknown to HOPS | exclusion |
| d-path-free | unknown to HOPS | unknown to HOPS |
| degeneracy | unknown to HOPS | unknown to HOPS |
| degree treewidth | unknown to HOPS | exclusion |
| diameter | exclusion | unknown to HOPS |
| diameter+max degree | unknown to HOPS | exclusion |
| disjoint cycles | unknown to HOPS | unknown to HOPS |
| distance to bipartite | exclusion | unknown to HOPS |
| distance to block | exclusion | unknown to HOPS |
| distance to bounded components | unknown to HOPS | unknown to HOPS |
| distance to chordal | exclusion | unknown to HOPS |
| distance to cluster | exclusion | unknown to HOPS |
| distance to co-cluster | exclusion | unknown to HOPS |
| distance to cograph | exclusion | unknown to HOPS |
| distance to complete | exclusion | unknown to HOPS |
| distance to edgeless | unknown to HOPS | unknown to HOPS |
| distance to forest | unknown to HOPS | unknown to HOPS |
| distance to interval | exclusion | unknown to HOPS |
| distance to linear forest | unknown to HOPS | unknown to HOPS |
| distance to maximum degree | unknown to HOPS | unknown to HOPS |
| distance to outerplanar | unknown to HOPS | unknown to HOPS |
| distance to perfect | exclusion | unknown to HOPS |
| distance to planar | unknown to HOPS | unknown to HOPS |
| distance to stars | unknown to HOPS | unknown to HOPS |
| domatic number | exclusion | unknown to HOPS |
| domination number | exclusion | unknown to HOPS |
| edge clique cover number | exclusion | unknown to HOPS |
| edge connectivity | unknown to HOPS | unknown to HOPS |
| edgeless | unknown to HOPS | exclusion |
| feedback edge set | unknown to HOPS | exclusion |
| feedback vertex set | unknown to HOPS | unknown to HOPS |
| forest | unknown to HOPS | exclusion |
| genus | unknown to HOPS | unknown to HOPS |
| girth | exclusion | unknown to HOPS |
| grid | unknown to HOPS | exclusion |
| h-index | unknown to HOPS | unknown to HOPS |
| inf-flip-width | exclusion | unknown to HOPS |
| interval | unknown to HOPS | unknown to HOPS |
| iterated type partitions | exclusion | unknown to HOPS |
| linear clique-width | exclusion | unknown to HOPS |
| linear forest | unknown to HOPS | exclusion |
| linear NLC-width | exclusion | unknown to HOPS |
| linear rank-width | exclusion | unknown to HOPS |
| maximum clique | exclusion | unknown to HOPS |
| maximum degree | unknown to HOPS | exclusion |
| maximum independent set | exclusion | unknown to HOPS |
| maximum induced matching | exclusion | unknown to HOPS |
| maximum leaf number | unknown to HOPS | exclusion |
| maximum matching | unknown to HOPS | unknown to HOPS |
| maximum matching on bipartite graphs | unknown to HOPS | unknown to HOPS |
| mim-width | exclusion | unknown to HOPS |
| minimum degree | unknown to HOPS | unknown to HOPS |
| mm-width | unknown to HOPS | unknown to HOPS |
| modular-width | exclusion | unknown to HOPS |
| module-width | exclusion | unknown to HOPS |
| neighborhood diversity | exclusion | unknown to HOPS |
| NLC-width | exclusion | unknown to HOPS |
| NLCT-width | exclusion | unknown to HOPS |
| odd cycle transversal | exclusion | unknown to HOPS |
| outerplanar | unknown to HOPS | unknown to HOPS |
| path | unknown to HOPS | exclusion |
| pathwidth | unknown to HOPS | unknown to HOPS |
| pathwidth+maxdegree | unknown to HOPS | exclusion |
| perfect | unknown to HOPS | unknown to HOPS |
| planar | unknown to HOPS | unknown to HOPS |
| radius-r flip-width | exclusion | unknown to HOPS |
| rank-width | exclusion | unknown to HOPS |
| shrub-depth | exclusion | unknown to HOPS |
| sim-width | exclusion | unknown to HOPS |
| star | unknown to HOPS | exclusion |
| stars | unknown to HOPS | exclusion |
| topological bandwidth | unknown to HOPS | unknown to HOPS |
| tree | unknown to HOPS | exclusion |
| tree-independence number | unknown to HOPS | unknown to HOPS |
| treedepth | unknown to HOPS | unknown to HOPS |
| treelength | exclusion | unknown to HOPS |
| treewidth | unknown to HOPS | unknown to HOPS |
| twin-cover number | unknown to HOPS | unknown to HOPS |
| twin-width | exclusion | unknown to HOPS |
| vertex cover | unknown to HOPS | unknown to HOPS |
| vertex integrity | unknown to HOPS | unknown to HOPS |
Results
- 2022 Expanding the Graph Parameter Hierarchy by Tran
- page 34 : bounded c-closure does not imply bounded vertex connectivity – Observation 5.7. $c$-Closure is incomparable to Distance to Disconnected, Domatic Number and Maximum Clique.
- page 34 : bounded vertex connectivity does not imply bounded c-closure – Observation 5.7. $c$-Closure is incomparable to Distance to Disconnected, Domatic Number and Maximum Clique.
- Comparing Graph Parameters by Schröder
- page 16 : bounded distance to complete does not imply bounded vertex connectivity – Proposition 3.8
- page 20 : bounded distance to co-cluster does not imply bounded vertex connectivity – Proposition 3.12
- page 20 : bounded distance to bipartite does not imply bounded vertex connectivity – Proposition 3.12
- page 31 : bounded domatic number does not imply bounded vertex connectivity – Proposition 3.30