path
equivalent to: path
Relations
Other | Relation from | Relation to |
---|---|---|
acyclic chromatic number | exclusion | constant |
arboricity | exclusion | constant |
average degree | exclusion | constant |
average distance | exclusion | unknown to HOPS |
bandwidth | exclusion | unknown to HOPS |
bipartite | exclusion | inclusion |
bipartite number | exclusion | unknown to HOPS |
bisection bandwidth | exclusion | constant |
block | exclusion | inclusion |
book thickness | exclusion | constant |
boolean width | exclusion | constant |
bounded components | exclusion | unbounded |
boxicity | exclusion | constant |
branch width | exclusion | constant |
c-closure | exclusion | constant |
carving-width | exclusion | constant |
chordal | exclusion | inclusion |
chordality | exclusion | constant |
chromatic number | exclusion | constant |
clique cover number | exclusion | unbounded |
clique-tree-width | exclusion | constant |
clique-width | exclusion | constant |
cluster | exclusion | exclusion |
co-cluster | exclusion | exclusion |
cograph | exclusion | exclusion |
complete | exclusion | exclusion |
connected | exclusion | inclusion |
cutwidth | exclusion | constant |
cycle | unknown to HOPS | unknown to HOPS |
cycles | exclusion | unknown to HOPS |
d-path-free | exclusion | unbounded |
degeneracy | exclusion | constant |
degree treewidth | exclusion | constant |
diameter | exclusion | unbounded |
diameter+max degree | exclusion | unbounded |
disjoint cycles | exclusion | inclusion |
distance to bipartite | exclusion | constant |
distance to block | exclusion | constant |
distance to bounded components | exclusion | unbounded |
distance to chordal | exclusion | constant |
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 | constant |
distance to interval | exclusion | constant |
distance to linear forest | exclusion | constant |
distance to maximum degree | exclusion | constant |
distance to outerplanar | exclusion | constant |
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 | constant |
feedback vertex set | exclusion | constant |
forest | exclusion | inclusion |
genus | exclusion | constant |
girth | exclusion | unknown to HOPS |
grid | exclusion | inclusion |
h-index | exclusion | constant |
inf-flip-width | exclusion | constant |
interval | exclusion | inclusion |
iterated type partitions | exclusion | unbounded |
linear clique-width | exclusion | constant |
linear forest | unknown to HOPS | inclusion |
linear NLC-width | exclusion | constant |
linear rank-width | exclusion | constant |
maximum clique | exclusion | constant |
maximum degree | exclusion | constant |
maximum independent set | exclusion | unbounded |
maximum induced matching | exclusion | unbounded |
maximum leaf number | unknown to HOPS | unknown to HOPS |
maximum matching | exclusion | unbounded |
maximum matching on bipartite graphs | exclusion | unbounded |
mim-width | exclusion | constant |
minimum degree | exclusion | constant |
mm-width | exclusion | constant |
modular-width | exclusion | unbounded |
module-width | exclusion | constant |
neighborhood diversity | exclusion | unbounded |
NLC-width | exclusion | constant |
NLCT-width | exclusion | constant |
odd cycle transversal | exclusion | constant |
outerplanar | exclusion | inclusion |
pathwidth | exclusion | constant |
pathwidth+maxdegree | exclusion | constant |
perfect | exclusion | inclusion |
planar | exclusion | inclusion |
radius-r flip-width | exclusion | constant |
rank-width | exclusion | constant |
shrub-depth | exclusion | unknown to HOPS |
sim-width | exclusion | constant |
star | exclusion | exclusion |
stars | exclusion | exclusion |
topological bandwidth | exclusion | unknown to HOPS |
tree | exclusion | inclusion |
tree-independence number | exclusion | constant |
treedepth | exclusion | unbounded |
treelength | exclusion | unknown to HOPS |
treewidth | exclusion | constant |
twin-cover number | exclusion | unbounded |
twin-width | exclusion | constant |
vertex connectivity | exclusion | unknown to HOPS |
vertex cover | exclusion | unbounded |
vertex integrity | exclusion | unbounded |
Results
- 2022 Expanding the Graph Parameter Hierarchy by Tran
- page 24 : graph class path has unbounded modular-width – The Modular-width of a path $P$ with length $n > 3$ is $n$.
- page 26 : graph class path has unbounded neighborhood diversity – The Neighborhood Diversity of a Path $P$ with length $n > 3$ is $n$.
- 2010 Comparing 17 graph parameters by Sasák
- page 30 : graph class path has constant carving-width – … path with carving-width 2.
- unknown source
- graph class path has unbounded treedepth
- graph class path has unbounded distance to cluster – trivially
- graph class path has unbounded diameter – trivially
- graph class path has unbounded maximum matching
- assumed
- graph class path is included in graph class connected – by definition
- graph class path is included in graph class linear forest – by definition
- graph class path is included in graph class tree
- graph class tree is not included in graph class path
- graph class path is included in graph class grid
- graph class grid is not included in graph class path