pathwidth+maxdegree
tags: linear variant
equivalent to: pathwidth+maxdegree, cutwidth
Relations
| Other | Relation from | Relation to |
|---|---|---|
| acyclic chromatic number | exclusion | upper bound |
| arboricity | exclusion | upper bound |
| average degree | exclusion | upper bound |
| average distance | exclusion | exclusion |
| bandwidth | upper bound | unknown to HOPS |
| bipartite | unbounded | exclusion |
| bipartite number | exclusion | unknown to HOPS |
| bisection bandwidth | exclusion | unknown to HOPS |
| block | unbounded | exclusion |
| book thickness | exclusion | upper bound |
| boolean width | exclusion | upper bound |
| bounded components | upper bound | exclusion |
| boxicity | exclusion | upper bound |
| branch width | exclusion | upper bound |
| c-closure | exclusion | upper bound |
| carving-width | unknown to HOPS | upper bound |
| chordal | unbounded | exclusion |
| chordality | exclusion | upper bound |
| chromatic number | exclusion | upper bound |
| clique cover number | exclusion | exclusion |
| clique-tree-width | exclusion | upper bound |
| clique-width | exclusion | upper bound |
| cluster | unbounded | exclusion |
| co-cluster | unbounded | exclusion |
| cograph | unbounded | exclusion |
| complete | unbounded | exclusion |
| connected | unbounded | unknown to HOPS |
| cutwidth | upper bound | upper bound |
| cycle | constant | exclusion |
| cycles | constant | exclusion |
| d-path-free | exclusion | exclusion |
| degeneracy | exclusion | upper bound |
| degree treewidth | unknown to HOPS | upper bound |
| diameter | exclusion | exclusion |
| diameter+max degree | upper bound | exclusion |
| disjoint cycles | unbounded | exclusion |
| distance to bipartite | exclusion | exclusion |
| distance to block | exclusion | exclusion |
| distance to bounded components | exclusion | 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 | exclusion | exclusion |
| distance to forest | exclusion | exclusion |
| distance to interval | exclusion | exclusion |
| distance to linear forest | exclusion | exclusion |
| distance to maximum degree | exclusion | upper bound |
| distance to outerplanar | exclusion | exclusion |
| distance to perfect | exclusion | exclusion |
| distance to planar | exclusion | exclusion |
| distance to stars | exclusion | exclusion |
| domatic number | exclusion | upper bound |
| domination number | exclusion | exclusion |
| edge clique cover number | exclusion | exclusion |
| edge connectivity | exclusion | upper bound |
| edgeless | constant | exclusion |
| feedback edge set | exclusion | exclusion |
| feedback vertex set | exclusion | exclusion |
| forest | unbounded | exclusion |
| genus | exclusion | exclusion |
| girth | exclusion | exclusion |
| grid | unbounded | exclusion |
| h-index | exclusion | upper bound |
| inf-flip-width | exclusion | upper bound |
| interval | unbounded | exclusion |
| iterated type partitions | exclusion | exclusion |
| linear clique-width | exclusion | upper bound |
| linear forest | constant | exclusion |
| linear NLC-width | exclusion | upper bound |
| linear rank-width | exclusion | upper bound |
| maximum clique | exclusion | upper bound |
| maximum degree | exclusion | upper bound |
| maximum independent set | exclusion | exclusion |
| maximum induced matching | exclusion | exclusion |
| maximum leaf number | upper bound | exclusion |
| maximum matching | exclusion | exclusion |
| maximum matching on bipartite graphs | exclusion | exclusion |
| mim-width | exclusion | upper bound |
| minimum degree | exclusion | upper bound |
| mm-width | exclusion | upper bound |
| modular-width | exclusion | exclusion |
| module-width | exclusion | upper bound |
| neighborhood diversity | exclusion | exclusion |
| NLC-width | exclusion | upper bound |
| NLCT-width | exclusion | upper bound |
| odd cycle transversal | exclusion | exclusion |
| outerplanar | unbounded | exclusion |
| path | constant | exclusion |
| pathwidth | exclusion | upper bound |
| perfect | unbounded | exclusion |
| planar | unbounded | exclusion |
| radius-r flip-width | exclusion | upper bound |
| rank-width | exclusion | upper bound |
| shrub-depth | exclusion | unknown to HOPS |
| sim-width | exclusion | upper bound |
| star | unbounded | exclusion |
| stars | unbounded | exclusion |
| topological bandwidth | unknown to HOPS | unknown to HOPS |
| tree | unbounded | exclusion |
| tree-independence number | exclusion | upper bound |
| treedepth | exclusion | exclusion |
| treelength | exclusion | unknown to HOPS |
| treewidth | exclusion | upper bound |
| twin-cover number | exclusion | exclusion |
| twin-width | exclusion | upper bound |
| vertex connectivity | exclusion | unknown to HOPS |
| vertex cover | exclusion | exclusion |
| vertex integrity | exclusion | exclusion |
Results
- 1998 A partial $k$-arboretum of graphs with bounded treewidth by Bodlaender
- page 24 : pathwidth+maxdegree upper bounds cutwidth by a linear function – Theorem 49.
- page 24 : cutwidth upper bounds pathwidth+maxdegree by a linear function – Theorem 49.
- assumed
- pathwidth+maxdegree upper bounds pathwidth by a linear function – by definition
- pathwidth+maxdegree upper bounds maximum degree by a linear function – by definition