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A permutation graph can be defined as an intersection graph of segments whoseendpoints lie on two parallel lines $\ell_1$ and $\ell_2$, one on each. Abipartite 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 abipartite permutation graph. This problem is NP-complete but it does admit anFPT algorithm parameterized by $k$.  In this paper we study the kernelization of this problem and show that itadmits a polynomial kernel with $O(k^{62})$ vertices.

A polynomial kernel for vertex deletion into bipartite permutation graphs