I
NSTANCE
:
Graph
, a weight function
, and an
integer
.
S
OLUTION
:
A partition of
V
into
k
disjoint sets
.
M
EASURE
:
The sum of the weight of the edges between the disjoint sets, i.e.,
Good News:
Approximable within
[
116
] and [
265
].
Bad News:
A
PX
-complete.
Comment:
The unweighted version is equivalent to M
AXIMUM
K
-C
OLORABLE
S
UBGRAPH
.
Approximable within 1.21 for
k=3
, 1.18 for
k=4
, and 1.15 for
k=5
[
116
].
Not approximable within
1+1/(34k)
[
204
].
The constrained variation in which the input is extended with a positive
integer
W
, a vertex
and a subset
S
of
V
, and the problem
is to find the 2-cut of weight at least
W
with the largest number of
vertices from
S
on the same side as
,
is not approximable within
for some
[
352
].