grid
equivalent to: grid
providers: ISGCI
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | exclusion | constant |
arboricity | exclusion | constant |
average degree | exclusion | constant |
average distance | exclusion | unbounded |
bandwidth | exclusion | unbounded |
bipartite | exclusion | inclusion |
bipartite number | exclusion | unknown to HOPS |
bisection bandwidth | exclusion | unbounded |
block | exclusion | exclusion |
book thickness | exclusion | constant |
boolean width | exclusion | unbounded |
bounded components | exclusion | unbounded |
boxicity | exclusion | constant |
branch width | exclusion | unbounded |
c-closure | exclusion | constant |
carving-width | exclusion | unbounded |
chordal | exclusion | exclusion |
chordality | exclusion | constant |
chromatic number | exclusion | constant |
clique cover number | exclusion | unbounded |
clique-tree-width | exclusion | unbounded |
clique-width | exclusion | unbounded |
cluster | exclusion | exclusion |
co-cluster | exclusion | exclusion |
cograph | exclusion | exclusion |
complete | exclusion | exclusion |
connected | exclusion | inclusion |
cutwidth | exclusion | unbounded |
cycle | unknown to HOPS | exclusion |
cycles | exclusion | exclusion |
d-path-free | exclusion | unbounded |
degeneracy | exclusion | constant |
degree treewidth | exclusion | unbounded |
diameter | exclusion | unbounded |
diameter+max degree | exclusion | unbounded |
disjoint cycles | exclusion | exclusion |
distance to bipartite | exclusion | constant |
distance to block | exclusion | unbounded |
distance to bounded components | exclusion | unbounded |
distance to chordal | exclusion | unbounded |
distance to cluster | exclusion | unbounded |
distance to co-cluster | exclusion | unbounded |
distance to cograph | exclusion | unbounded |
distance to complete | exclusion | unbounded |
distance to edgeless | exclusion | unbounded |
distance to forest | exclusion | unbounded |
distance to interval | exclusion | unbounded |
distance to linear forest | exclusion | unbounded |
distance to maximum degree | exclusion | constant |
distance to outerplanar | exclusion | unbounded |
distance to perfect | exclusion | constant |
distance to planar | exclusion | constant |
distance to stars | exclusion | unbounded |
domatic number | exclusion | constant |
domination number | exclusion | unbounded |
edge clique cover number | exclusion | unbounded |
edge connectivity | exclusion | constant |
edgeless | unknown to HOPS | exclusion |
feedback edge set | exclusion | unbounded |
feedback vertex set | exclusion | unbounded |
forest | exclusion | exclusion |
genus | exclusion | constant |
girth | exclusion | unknown to HOPS |
h-index | exclusion | constant |
inf-flip-width | exclusion | unbounded |
interval | exclusion | exclusion |
iterated type partitions | exclusion | unbounded |
linear clique-width | exclusion | unbounded |
linear forest | unknown to HOPS | exclusion |
linear NLC-width | exclusion | unbounded |
linear rank-width | exclusion | unbounded |
maximum clique | exclusion | constant |
maximum degree | exclusion | constant |
maximum independent set | exclusion | unbounded |
maximum induced matching | exclusion | unbounded |
maximum leaf number | unknown to HOPS | unbounded |
maximum matching | exclusion | unbounded |
maximum matching on bipartite graphs | exclusion | unbounded |
mim-width | exclusion | unknown to HOPS |
minimum degree | exclusion | constant |
mm-width | exclusion | unbounded |
modular-width | exclusion | unbounded |
module-width | exclusion | unbounded |
neighborhood diversity | exclusion | unbounded |
NLC-width | exclusion | unbounded |
NLCT-width | exclusion | unbounded |
odd cycle transversal | exclusion | constant |
outerplanar | exclusion | exclusion |
path | inclusion | exclusion |
pathwidth | exclusion | unbounded |
pathwidth+maxdegree | exclusion | unbounded |
perfect | exclusion | inclusion |
planar | exclusion | inclusion |
radius-r flip-width | exclusion | constant |
rank-width | exclusion | unbounded |
shrub-depth | exclusion | unbounded |
sim-width | exclusion | unknown to HOPS |
star | exclusion | exclusion |
stars | exclusion | exclusion |
topological bandwidth | exclusion | unbounded |
tree | exclusion | exclusion |
tree-independence number | exclusion | unknown to HOPS |
treedepth | exclusion | unbounded |
treelength | exclusion | unknown to HOPS |
treewidth | exclusion | unbounded |
twin-cover number | exclusion | unbounded |
twin-width | exclusion | constant |
vertex connectivity | exclusion | unknown to HOPS |
vertex cover | exclusion | unbounded |
vertex integrity | exclusion | unbounded |
Results
- 2021 Twin-width I: Tractable
FO
Model Checking by Bonnet, Kim, Thomassé, Watrigant- page 15 : graph class grid has constant twin-width – Theorem 4.3. For every positive integers $d$ and $n$, the $d$-dimensional $n$-grid has twin-width at most $3d$.
- 2010 Comparing 17 graph parameters by Sasák
- 2010 The rank-width of the square grid by Jelínek
- page 2 : graph class grid has unbounded rank-width – The grid $G_{n,n}$ has rank-width equal to $n-1$.
- 1998 A partial $k$-arboretum of graphs with bounded treewidth by Bodlaender
- unknown source
- graph class grid has unbounded distance to chordal
- graph class grid has unbounded average distance
- graph class grid has unbounded bisection bandwidth
- graph class grid has constant maximum degree
- assumed
- grid – Cartesian product of two paths.
- graph class grid is included in graph class planar
- graph class planar is not included in graph class grid
- graph class grid is included in graph class bipartite
- graph class bipartite is not included in graph class grid
- graph class grid is included in graph class connected
- graph class connected is not included in graph class grid
- graph class path is included in graph class grid
- graph class grid is not included in graph class path
- graph class grid has constant maximum degree – By definition