  The aim of this note is to provide a reduction of the Exact Matching problem
to the Top-$k$ Perfect Matching Problem. Together with earlier work by El
Maalouly, this shows that the two problems are polynomial-time equivalent.
  The Exact Matching Problem is a well-known 40 years old problem for which a
randomized, but no deterministic poly-time algorithm has been discovered. The
Top-$k$ Perfect Matching Problem is the problem of finding a perfect matching
which maximizes the total weight of the $k$ heaviest edges contained in it.
