clique-tree-width
equivalent to: NLCT-width, clique-tree-width
Relations
| Other | Relation from | Relation to |
|---|---|---|
| acyclic chromatic number | exclusion | exclusion |
| arboricity | exclusion | exclusion |
| average degree | exclusion | exclusion |
| average distance | exclusion | exclusion |
| bandwidth | upper bound | exclusion |
| bipartite | unbounded | exclusion |
| bipartite number | exclusion | unknown to HOPS |
| bisection bandwidth | exclusion | exclusion |
| block | unknown to HOPS | exclusion |
| book thickness | exclusion | exclusion |
| boolean width | unknown to HOPS | upper bound |
| bounded components | upper bound | exclusion |
| boxicity | exclusion | unknown to HOPS |
| branch width | upper bound | exclusion |
| c-closure | exclusion | exclusion |
| carving-width | upper bound | exclusion |
| chordal | unknown to HOPS | exclusion |
| chordality | exclusion | unknown to HOPS |
| chromatic number | exclusion | exclusion |
| clique cover number | exclusion | exclusion |
| clique-width | unknown to HOPS | upper bound |
| cluster | constant | exclusion |
| co-cluster | unknown to HOPS | exclusion |
| cograph | unknown to HOPS | exclusion |
| complete | constant | exclusion |
| connected | unbounded | unknown to HOPS |
| cutwidth | upper bound | exclusion |
| cycle | constant | exclusion |
| cycles | constant | exclusion |
| d-path-free | upper bound | exclusion |
| degeneracy | exclusion | 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 | unknown to HOPS | exclusion |
| distance to bounded components | upper bound | exclusion |
| distance to chordal | exclusion | exclusion |
| distance to cluster | unknown to HOPS | exclusion |
| distance to co-cluster | unknown to HOPS | exclusion |
| distance to cograph | unknown to HOPS | exclusion |
| distance to complete | upper bound | 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 | exclusion | exclusion |
| distance to outerplanar | upper bound | exclusion |
| distance to perfect | exclusion | exclusion |
| distance to planar | exclusion | exclusion |
| distance to stars | upper bound | exclusion |
| domatic number | exclusion | exclusion |
| domination number | exclusion | exclusion |
| edge clique cover number | upper bound | exclusion |
| edge connectivity | exclusion | exclusion |
| edgeless | constant | exclusion |
| feedback edge set | upper bound | exclusion |
| feedback vertex set | upper bound | exclusion |
| forest | constant | exclusion |
| genus | exclusion | exclusion |
| girth | exclusion | exclusion |
| grid | unbounded | exclusion |
| h-index | exclusion | exclusion |
| inf-flip-width | unknown to HOPS | upper bound |
| interval | unknown to HOPS | exclusion |
| iterated type partitions | unknown to HOPS | exclusion |
| linear clique-width | upper bound | unknown to HOPS |
| linear forest | constant | exclusion |
| linear NLC-width | upper bound | unknown to HOPS |
| linear rank-width | upper bound | unknown to HOPS |
| maximum clique | exclusion | exclusion |
| maximum degree | exclusion | 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 | unknown to HOPS | upper bound |
| minimum degree | exclusion | exclusion |
| mm-width | upper bound | exclusion |
| modular-width | unknown to HOPS | exclusion |
| module-width | unknown to HOPS | upper bound |
| neighborhood diversity | upper bound | exclusion |
| NLC-width | unknown to HOPS | upper bound |
| NLCT-width | upper bound | upper bound |
| odd cycle transversal | exclusion | exclusion |
| outerplanar | constant | exclusion |
| path | constant | exclusion |
| pathwidth | upper bound | exclusion |
| pathwidth+maxdegree | upper bound | exclusion |
| perfect | unbounded | exclusion |
| planar | unbounded | exclusion |
| radius-r flip-width | exclusion | upper bound |
| rank-width | unknown to HOPS | upper bound |
| shrub-depth | upper bound | unknown to HOPS |
| sim-width | unknown to HOPS | upper bound |
| 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 | upper bound | exclusion |
| twin-width | exclusion | upper bound |
| vertex connectivity | unknown to HOPS | exclusion |
| vertex cover | upper bound | exclusion |
| vertex integrity | upper bound | exclusion |
Results
- 2005 On the relationship between NLC-width and linear NLC-width by Gurski, Wanke
- page 4 : clique-tree-width – Definition 5
- page 8 : linear clique-width upper bounds clique-tree-width by a linear function
- page 8 : clique-tree-width upper bounds clique-width by a linear function
- page 8 : clique-tree-width upper bounds NLCT-width by a linear function
- page 8 : NLCT-width upper bounds clique-tree-width by a linear function