maximum matching on bipartite graphs

Definition: an intersetcion of bipartite, and maximum matching

Relations

Other		Relation from	Relation to
acyclic chromatic number	red■	exclusion	upper bound
admissibility	red■	exclusion	upper bound
arboricity	red■	exclusion	upper bound
average degree	red■	exclusion	upper bound
average distance	red■	exclusion	upper bound
bandwidth	blue■	exclusion	exclusion
bipartite	red■	unbounded	upper bound
bipartite number	blue■	exclusion	exclusion
bisection bandwidth	magenta■	exclusion	unknown to HOPS
block	magenta■	unbounded	unknown to HOPS
book thickness	red■	exclusion	upper bound
boolean width	red■	exclusion	upper bound
bounded components	blue■	exclusion	exclusion
bounded expansion	red■	exclusion	upper bound
boxicity	red■	exclusion	upper bound
branch width	red■	exclusion	upper bound
c-closure	magenta■	exclusion	unknown to HOPS
carving-width	blue■	exclusion	exclusion
chi-bounded	red■	exclusion	upper bound
chordal	magenta■	unbounded	unknown to HOPS
chordality	red■	exclusion	upper bound
chromatic number	red■	exclusion	upper bound
clique cover number	blue■	exclusion	exclusion
clique-tree-width	red■	exclusion	upper bound
clique-width	red■	exclusion	upper bound
cluster	magenta■	unbounded	unknown to HOPS
co-cluster	magenta■	unbounded	unknown to HOPS
cograph	magenta■	unbounded	unknown to HOPS
complete	blue■	unbounded	exclusion
connected	blue■	exclusion	avoids
contraction complexity	blue■	exclusion	exclusion
cutwidth	blue■	exclusion	exclusion
cycle	cyan■	unknown to HOPS	exclusion
cycles	blue■	unbounded	exclusion
d-admissibility	red■	exclusion	upper bound
d-path-free	red■	exclusion	upper bound
degeneracy	red■	exclusion	upper bound
degree treewidth	blue■	exclusion	exclusion
diameter	red■	exclusion	upper bound
diameter+max degree	blue■	exclusion	exclusion
distance to bipartite	red■	exclusion	upper bound
distance to block	red■	exclusion	upper bound
distance to bounded components	red■	exclusion	upper bound
distance to chordal	red■	exclusion	upper bound
distance to cluster	red■	exclusion	upper bound
distance to co-cluster	red■	exclusion	upper bound
distance to cograph	red■	exclusion	upper bound
distance to complete	blue■	exclusion	exclusion
distance to edgeless	red■	exclusion	tight bounds
distance to forest	red■	exclusion	upper bound
distance to interval	red■	exclusion	upper bound
distance to linear forest	red■	exclusion	upper bound
distance to maximum degree	red■	exclusion	upper bound
distance to outerplanar	red■	exclusion	upper bound
distance to perfect	red■	exclusion	upper bound
distance to planar	red■	exclusion	upper bound
distance to stars	red■	exclusion	upper bound
domatic number	red■	exclusion	upper bound
domination number	blue■	exclusion	exclusion
domino treewidth	blue■	exclusion	exclusion
edge clique cover number	magenta■	exclusion	unknown to HOPS
edge connectivity	red■	exclusion	upper bound
edge-cut width	magenta■	exclusion	unknown to HOPS
edge-treewidth	magenta■	exclusion	unknown to HOPS
edgeless	green■	upper bound	avoids
excluded minor	magenta■	exclusion	unknown to HOPS
excluded planar minor	gray■	unknown to HOPS	unknown to HOPS
excluded top-minor	red■	exclusion	upper bound
feedback edge set	magenta■	exclusion	unknown to HOPS
feedback vertex set	red■	exclusion	upper bound
flip-width	red■	exclusion	upper bound
forest	magenta■	unbounded	unknown to HOPS
genus	magenta■	exclusion	unknown to HOPS
grid	blue■	unbounded	exclusion
h-index	red■	exclusion	upper bound
interval	magenta■	unbounded	unknown to HOPS
iterated type partitions	red■	exclusion	upper bound
linear clique-width	red■	exclusion	upper bound
linear forest	blue■	unbounded	exclusion
linear NLC-width	red■	exclusion	upper bound
linear rank-width	red■	exclusion	upper bound
maximum clique	red■	exclusion	upper bound
maximum degree	blue■	exclusion	exclusion
maximum independent set	blue■	exclusion	exclusion
maximum induced matching	red■	exclusion	upper bound
maximum leaf number	blue■	exclusion	exclusion
maximum matching	red■	exclusion	upper bound
maximum matching on bipartite graphs	yellow■	equal	equal
merge-width	red■	exclusion	upper bound
mim-width	red■	exclusion	upper bound
minimum degree	red■	exclusion	upper bound
mm-width	red■	exclusion	upper bound
modular-width	red■	exclusion	upper bound
module-width	red■	exclusion	upper bound
monadically dependent	red■	exclusion	upper bound
monadically stable	red■	exclusion	upper bound
neighborhood diversity	red■	exclusion	upper bound
NLC-width	red■	exclusion	upper bound
NLCT-width	red■	exclusion	upper bound
nowhere dense	red■	exclusion	upper bound
odd cycle transversal	red■	exclusion	upper bound
outerplanar	gray■	unknown to HOPS	unknown to HOPS
overlap treewidth	magenta■	exclusion	unknown to HOPS
path	blue■	unbounded	exclusion
pathwidth	red■	exclusion	upper bound
pathwidth+maxdegree	blue■	exclusion	exclusion
perfect	red■	unbounded	upper bound
planar	magenta■	unbounded	unknown to HOPS
radius-inf flip-width	red■	exclusion	upper bound
radius-r flip-width	red■	exclusion	upper bound
rank-width	red■	exclusion	upper bound
series-parallel	gray■	unknown to HOPS	unknown to HOPS
shrub-depth	red■	exclusion	upper bound
sim-width	red■	exclusion	upper bound
size	blue■	exclusion	exclusion
slim tree-cut width	magenta■	exclusion	unknown to HOPS
sparse twin-width	red■	exclusion	upper bound
star	green■	upper bound	exclusion
stars	magenta■	unbounded	unknown to HOPS
strong coloring number	red■	exclusion	upper bound
strong d-coloring number	red■	exclusion	upper bound
strong inf-coloring number	red■	exclusion	upper bound
topological bandwidth	magenta■	exclusion	unknown to HOPS
tree	blue■	unbounded	exclusion
tree-cut width	magenta■	exclusion	unknown to HOPS
tree-independence number	red■	exclusion	upper bound
tree-partition-width	magenta■	exclusion	unknown to HOPS
treebandwidth	magenta■	exclusion	unknown to HOPS
treedepth	red■	exclusion	upper bound
treelength	red■	exclusion	upper bound
treespan	blue■	exclusion	exclusion
treewidth	red■	exclusion	upper bound
twin-cover number	red■	exclusion	upper bound
twin-width	red■	exclusion	upper bound
vertex connectivity	gray■	unknown to HOPS	unknown to HOPS
vertex cover	red■	exclusion	tight bounds
vertex integrity	red■	exclusion	upper bound
weak coloring number	red■	exclusion	upper bound
weak d-coloring number	red■	exclusion	upper bound
weak inf-coloring number	red■	exclusion	upper bound
weakly sparse	red■	exclusion	upper bound
weakly sparse and merge width	red■	exclusion	upper bound

Results

unknown source
- maximum matching on bipartite graphs upper and lower bounds vertex cover by a linear function – Kőnig’s theorem
assumed
- maximum matching on bipartite graphs upper bounds bipartite by a linear function – by definition
- maximum matching on bipartite graphs upper bounds maximum matching by a linear function – by definition
- maximum matching on bipartite graphs is equivalent to maximum matching on bipartite graphs – assumed