clique-width

abbr: cw

equivalent to: rank-width, inf-flip-width, NLC-width, module-width, boolean width

providers: ISGCI

Relations

Other		Relation from	Relation to
acyclic chromatic number	blue■	exclusion	exclusion
arboricity	blue■	exclusion	exclusion
average degree	blue■	exclusion	exclusion
average distance	blue■	exclusion	exclusion
bandwidth	green■	upper bound	exclusion
bipartite	blue■	unbounded	exclusion
bipartite number	magenta■	exclusion	unknown to HOPS
bisection bandwidth	blue■	exclusion	exclusion
block	cyan■	unknown to HOPS	exclusion
book thickness	blue■	exclusion	exclusion
boolean width	yellow■	upper bound	upper bound
bounded components	green■	upper bound	exclusion
boxicity	blue■	exclusion	exclusion
branch width	green■	upper bound	exclusion
c-closure	blue■	exclusion	exclusion
carving-width	green■	upper bound	exclusion
chordal	cyan■	unknown to HOPS	exclusion
chordality	blue■	exclusion	exclusion
chromatic number	blue■	exclusion	exclusion
clique cover number	blue■	exclusion	exclusion
clique-tree-width	lime■	upper bound	unknown to HOPS
clique-width	yellow■	equal	equal
cluster	green■	upper bound	exclusion
co-cluster	green■	upper bound	exclusion
cograph	green■	upper bound	exclusion
complete	green■	upper bound	exclusion
connected	blue■	unbounded	exclusion
contraction complexity	green■	upper bound	exclusion
cutwidth	green■	upper bound	exclusion
cycle	green■	upper bound	exclusion
cycles	green■	upper bound	exclusion
d-path-free	green■	upper bound	exclusion
degeneracy	blue■	exclusion	exclusion
degree treewidth	green■	upper bound	exclusion
diameter	blue■	exclusion	exclusion
diameter+max degree	green■	upper bound	exclusion
disconnected	cyan■	unknown to HOPS	exclusion
disjoint cycles	green■	upper bound	exclusion
distance to bipartite	blue■	exclusion	exclusion
distance to block	cyan■	unknown to HOPS	exclusion
distance to bounded components	green■	upper bound	exclusion
distance to chordal	blue■	exclusion	exclusion
distance to cluster	green■	upper bound	exclusion
distance to co-cluster	green■	upper bound	exclusion
distance to cograph	green■	upper bound	exclusion
distance to complete	green■	upper bound	exclusion
distance to disconnected	blue■	exclusion	exclusion
distance to edgeless	green■	upper bound	exclusion
distance to forest	green■	upper bound	exclusion
distance to interval	blue■	exclusion	exclusion
distance to linear forest	green■	upper bound	exclusion
distance to maximum degree	blue■	exclusion	exclusion
distance to outerplanar	green■	upper bound	exclusion
distance to perfect	blue■	exclusion	exclusion
distance to planar	blue■	exclusion	exclusion
distance to stars	green■	upper bound	exclusion
domatic number	blue■	exclusion	exclusion
domination number	blue■	exclusion	exclusion
edge clique cover number	green■	upper bound	exclusion
edge connectivity	blue■	exclusion	exclusion
edgeless	green■	upper bound	exclusion
feedback edge set	green■	upper bound	exclusion
feedback vertex set	green■	upper bound	exclusion
forest	green■	upper bound	exclusion
genus	blue■	exclusion	exclusion
girth	blue■	exclusion	exclusion
grid	blue■	unbounded	exclusion
h-index	blue■	exclusion	exclusion
inf-flip-width	yellow■	upper bound	upper bound
interval	cyan■	unknown to HOPS	exclusion
iterated type partitions	green■	upper bound	exclusion
linear clique-width	lime■	upper bound	unknown to HOPS
linear forest	green■	upper bound	exclusion
linear NLC-width	lime■	upper bound	unknown to HOPS
linear rank-width	lime■	upper bound	unknown to HOPS
maximum clique	blue■	exclusion	exclusion
maximum degree	blue■	exclusion	exclusion
maximum independent set	blue■	exclusion	exclusion
maximum induced matching	blue■	exclusion	exclusion
maximum leaf number	green■	upper bound	exclusion
maximum matching	green■	upper bound	exclusion
maximum matching on bipartite graphs	green■	upper bound	exclusion
mim-width	orange■	unknown to HOPS	upper bound
minimum degree	blue■	exclusion	exclusion
mm-width	green■	upper bound	exclusion
modular-width	green■	upper bound	exclusion
module-width	yellow■	upper bound	upper bound
neighborhood diversity	green■	upper bound	exclusion
NLC-width	yellow■	upper bound	upper bound
NLCT-width	lime■	upper bound	unknown to HOPS
odd cycle transversal	blue■	exclusion	exclusion
outerplanar	green■	upper bound	exclusion
path	green■	upper bound	exclusion
pathwidth	green■	upper bound	exclusion
pathwidth+maxdegree	green■	upper bound	exclusion
perfect	blue■	unbounded	exclusion
planar	blue■	unbounded	exclusion
radius-r flip-width	red■	exclusion	upper bound
rank-width	yellow■	tight bounds	upper bound
shrub-depth	green■	upper bound	exclusion
sim-width	orange■	unknown to HOPS	upper bound
size	green■	upper bound	exclusion
star	green■	upper bound	exclusion
stars	green■	upper bound	exclusion
topological bandwidth	green■	upper bound	exclusion
tree	green■	upper bound	exclusion
tree-independence number	gray■	unknown to HOPS	unknown to HOPS
treedepth	green■	upper bound	exclusion
treelength	magenta■	exclusion	unknown to HOPS
treewidth	green■	upper bound	exclusion
twin-cover number	green■	upper bound	exclusion
twin-width	red■	exclusion	upper bound
vertex connectivity	blue■	exclusion	exclusion
vertex cover	green■	upper bound	exclusion
vertex integrity	green■	upper bound	exclusion

Results

2022 Expanding the Graph Parameter Hierarchy by Tran
- page 25 : modular-width upper bounds clique-width by a computable function – Proposition 4.6. Modular-width strictly upper bounds Clique-width.
- page 25 : bounded clique-width does not imply bounded modular-width – Proposition 4.6. Modular-width strictly upper bounds Clique-width.
- page 36 : clique-width upper bounds twin-width by a tower function – Proposition 6.2. Clique-width strictly upper bounds Twin-width.
- page 36 : bounded twin-width does not imply bounded clique-width – Proposition 6.2. Clique-width strictly upper bounds Twin-width.
2019 The Graph Parameter Hierarchy by Sorge
- page 9 : distance to cograph upper bounds clique-width by an exponential function – Lemma 4.17. The distance $c$ to a cograph upper bounds the cliquewidth $q$. We have $q \le 2^{3+c}-1$.
2012 Twin-Cover: Beyond Vertex Cover in Parameterized Algorithmics by Ganian
- page 263 : twin-cover number upper bounds clique-width by a constant – The clique-width of graphs of twin-cover $k$ is at most $k+2$.
2006 Approximating clique-width and branch-width by Oum, Seymour
- page 9 : rank-width upper and lower bounds clique-width by an exponential function – Proposition 6.3
- page 9 : clique-width upper bounds rank-width by a linear function – Proposition 6.3
2005 On the relationship between NLC-width and linear NLC-width by Gurski, Wanke
- page 8 : clique-tree-width upper bounds clique-width by a linear function
2000 Upper bounds to the clique width of graphs by Courcelle, Olariu
- page 18 : treewidth upper bounds clique-width by an exponential function – We will prove that for every undirected graph $G$, $cwd(G) \le 2^{twd(G)+1}+1$ …
1998 Clique-decomposition, NLC-decomposition and modular decomposition—relationships and results for random graphs by Johansson
- clique-width upper bounds NLC-width by a linear function
- NLC-width upper bounds clique-width by a linear function
Comparing Graph Parameters by Schröder
- page 16 : bounded clique cover number does not imply bounded clique-width – Proposition 3.9
- page 23 : bounded genus does not imply bounded clique-width – Proposition 3.17
- page 23 : bounded distance to planar does not imply bounded clique-width – Proposition 3.17
- page 28 : bounded maximum degree does not imply bounded clique-width – Proposition 3.26
- page 28 : bounded distance to bipartite does not imply bounded clique-width – Proposition 3.26
- page 33 : bounded bisection bandwidth does not imply bounded clique-width – Proposition 3.32
assumed
- clique-width is equivalent to clique-width – assumed
unknown source
- linear clique-width upper bounds clique-width by a linear function
- clique-width upper bounds boolean width by a linear function
- boolean width upper bounds clique-width by an exponential function
- module-width upper bounds clique-width by a computable function
- clique-width upper bounds module-width by a computable function
- modular-width upper bounds clique-width by a computable function
- clique-width upper bounds mim-width by a linear function
- clique-width upper bounds twin-width by a tower function