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