radius-r flip-width
equivalent to: radius-r flip-width
Relations
| Other | Relation from | Relation to |
|---|---|---|
| acyclic chromatic number | unknown to HOPS | exclusion |
| arboricity | unknown to HOPS | exclusion |
| average degree | unknown to HOPS | exclusion |
| average distance | unknown to HOPS | exclusion |
| bandwidth | upper bound | exclusion |
| bipartite | unknown to HOPS | exclusion |
| bipartite number | unknown to HOPS | unknown to HOPS |
| bisection bandwidth | unknown to HOPS | exclusion |
| block | unknown to HOPS | exclusion |
| book thickness | unknown to HOPS | exclusion |
| boolean width | upper bound | exclusion |
| bounded components | upper bound | exclusion |
| boxicity | unknown to HOPS | exclusion |
| branch width | upper bound | exclusion |
| c-closure | unknown to HOPS | exclusion |
| carving-width | upper bound | exclusion |
| chordal | unknown to HOPS | exclusion |
| chordality | unknown to HOPS | exclusion |
| chromatic number | unknown to HOPS | exclusion |
| clique cover number | unknown to HOPS | exclusion |
| clique-tree-width | upper bound | exclusion |
| clique-width | upper bound | exclusion |
| cluster | constant | exclusion |
| co-cluster | constant | exclusion |
| cograph | constant | exclusion |
| complete | constant | exclusion |
| connected | unknown to HOPS | unknown to HOPS |
| cutwidth | upper bound | exclusion |
| cycle | constant | exclusion |
| cycles | constant | exclusion |
| d-path-free | upper bound | exclusion |
| degeneracy | unknown to HOPS | exclusion |
| degree treewidth | upper bound | exclusion |
| diameter | unknown to HOPS | exclusion |
| diameter+max degree | upper bound | exclusion |
| disjoint cycles | constant | exclusion |
| distance to bipartite | unknown to HOPS | exclusion |
| distance to block | unknown to HOPS | exclusion |
| distance to bounded components | upper bound | exclusion |
| distance to chordal | unknown to HOPS | exclusion |
| distance to cluster | unknown to HOPS | exclusion |
| distance to co-cluster | upper bound | exclusion |
| distance to cograph | upper bound | exclusion |
| distance to complete | upper bound | exclusion |
| distance to edgeless | upper bound | exclusion |
| distance to forest | upper bound | exclusion |
| distance to interval | unknown to HOPS | exclusion |
| distance to linear forest | upper bound | exclusion |
| distance to maximum degree | unknown to HOPS | exclusion |
| distance to outerplanar | upper bound | exclusion |
| distance to perfect | unknown to HOPS | exclusion |
| distance to planar | upper bound | exclusion |
| distance to stars | upper bound | exclusion |
| domatic number | unknown to HOPS | exclusion |
| domination number | unknown to HOPS | exclusion |
| edge clique cover number | upper bound | exclusion |
| edge connectivity | unknown to HOPS | exclusion |
| edgeless | constant | exclusion |
| feedback edge set | upper bound | exclusion |
| feedback vertex set | upper bound | exclusion |
| forest | constant | exclusion |
| genus | upper bound | exclusion |
| girth | unknown to HOPS | exclusion |
| grid | constant | exclusion |
| h-index | unknown to HOPS | exclusion |
| inf-flip-width | upper bound | exclusion |
| interval | unknown to HOPS | exclusion |
| iterated type partitions | upper bound | exclusion |
| linear clique-width | upper bound | exclusion |
| linear forest | constant | exclusion |
| linear NLC-width | upper bound | exclusion |
| linear rank-width | upper bound | exclusion |
| maximum clique | unknown to HOPS | exclusion |
| maximum degree | unknown to HOPS | exclusion |
| maximum independent set | unknown to HOPS | exclusion |
| maximum induced matching | unknown to HOPS | 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 | unknown to HOPS |
| minimum degree | unknown to HOPS | exclusion |
| mm-width | upper bound | exclusion |
| modular-width | upper bound | exclusion |
| module-width | upper bound | exclusion |
| neighborhood diversity | upper bound | exclusion |
| NLC-width | upper bound | exclusion |
| NLCT-width | upper bound | exclusion |
| odd cycle transversal | unknown to HOPS | exclusion |
| outerplanar | constant | exclusion |
| path | constant | exclusion |
| pathwidth | upper bound | exclusion |
| pathwidth+maxdegree | upper bound | exclusion |
| perfect | unknown to HOPS | exclusion |
| planar | constant | exclusion |
| rank-width | upper bound | exclusion |
| shrub-depth | upper bound | exclusion |
| sim-width | unknown to HOPS | 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 | unknown to HOPS | unknown to HOPS |
| treewidth | upper bound | exclusion |
| twin-cover number | upper bound | exclusion |
| twin-width | upper bound | unknown to HOPS |
| vertex connectivity | unknown to HOPS | exclusion |
| vertex cover | upper bound | exclusion |
| vertex integrity | upper bound | exclusion |
Results
- 2023 Flip-width: Cops and Robber on dense graphs by Toruńczyk
- radius-r flip-width – The radius-$r$ flip-width of a graph $G$, denoted $fwr (G)$, is the smallest number $k \in \mathbb{N}$ such that the cops have a winning strategy in the flipper game of radius $r$ and width $k$ on $G$
- twin-width upper bounds radius-r flip-width by an exponential function – Theorem 7.1. Fix $r \in \mathbb N$. For every graph $G$ of twin-width $d$ we have: $\mathrm{fw}_r(G) \le 2^d \cdot d^{O(r)}$.
- inf-flip-width upper bounds radius-r flip-width by a linear function – By definition