  IV-matching is a generalization of perfect bipartite matching. The complexity
of finding IV-matching in a graph was posted as an open problem at the ICALP
2014 conference.
  In this note, we resolve the question and prove that, contrary to the
expectations of the authors, the given problem is strongly NP-hard (already in
the simplest non-trivial case of four layers). Hence it is unlikely that there
would be an efficient (polynomial or pseudo-polynomial) algorithm solving the
problem.
