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GT11 MAXIMUM H-MATCHING
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Covering and Partitioning
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GT9 MINIMUM FEEDBACK
-
I
NSTANCE
:
Graph
.
-
S
OLUTION
:
A triangle packing for
G
, i.e., a collection
of
disjoint subsets of
V
, each containing exactly 3 vertices, such that
for each
,
, all three of the edges
,
, and
belong to
E
.
-
M
EASURE
:
Cardinality of the triangle packing, i.e., the number of disjoint subsets
.
-
Good News:
Approximable within 3/2
for any
[
182
].
-
Bad News:
A
PX
-complete [
198
].
-
Comment:
Transformation from bounded M
AXIMUM
3-D
IMENSIONAL
M
ATCHING
.
Admits a PTAS for planar graphs [
33
]
and for
-precision unit disk graphs [
181
].
Still A
PX
-complete when the degree of
G
is bounded by 4 [
198
].
-
Garey and Johnson:
GT11
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997