  A permutation graph can be defined as an intersection graph of segments whose
endpoints lie on two parallel lines $\ell_1$ and $\ell_2$, one on each. A
bipartite permutation graph is a permutation graph which is bipartite.
  In the the bipartite permutation vertex deletion problem we ask for a given
$n$-vertex graph, whether we can remove at most $k$ vertices to obtain a
bipartite permutation graph. This problem is NP-complete but it does admit an
FPT algorithm parameterized by $k$.
  In this paper we study the kernelization of this problem and show that it
admits a polynomial kernel with $O(k^{62})$ vertices.
