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