inf-flip-width

equivalent to: rank-width, clique-width, module-width, inf-flip-width, NLC-width, boolean 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	upper bound	upper bound
bounded components	upper bound	exclusion
boxicity	exclusion	exclusion
branch width	upper bound	exclusion
c-closure	exclusion	exclusion
carving-width	upper bound	exclusion
chordal	unknown to HOPS	exclusion
chordality	exclusion	exclusion
chromatic number	exclusion	exclusion
clique cover number	exclusion	exclusion
clique-tree-width	upper bound	unknown to HOPS
clique-width	upper bound	upper bound
cluster	constant	exclusion
co-cluster	constant	exclusion
cograph	constant	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	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	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
interval	unknown to HOPS	exclusion
iterated type partitions	upper bound	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	upper bound	exclusion
module-width	upper bound	upper bound
neighborhood diversity	upper bound	exclusion
NLC-width	upper bound	upper bound
NLCT-width	upper bound	unknown to HOPS
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	upper bound	upper bound
shrub-depth	upper bound	exclusion
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

2023 Flip-width: Cops and Robber on dense graphs by Toruńczyk
- inf-flip-width – See radius-r flip-width for $r=\infty$.
- inf-flip-width upper bounds rank-width by a linear function – For every graph $G$, we have $\mathrm{rankwidth}(G) \le 3 \mathrm{fw}_\infty(G)+1$ …
- rank-width upper bounds inf-flip-width by an exponential function – For every graph $G$, we have … $3 \mathrm{fw}_\infty(G)+1 \le O(2^{\mathrm{rankwidth(G)}})$.
- inf-flip-width upper bounds radius-r flip-width by a linear function – By definition