S
OLUTION
:
A partition of
V
into disjoint sets
A, B
, and
C
, such that
and
no edge has one endpoint in
A
and one in
B
.
M
EASURE
:
The size of the separator, i.e.,
|C|
.
Bad News:
Not approximable within
for any
,
even for graphs of maximum degree 3.
[
60
].
Comment:
For planar graphs a separator of size
can be found in
polynomial time [
260
].
An
f(|V|)
-approximation algorithm is also a
algorithm for
M
INIMUM
B
-B
ALANCED
C
UT
[
60
].