In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S ⊆ V (G) such that |S| ≤ k and G−S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that G − S be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time O(9k|V (G)|9). And they posed the question whether BPVD admits a polynomial kernel. We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G, k) of BPVD, in polynomial time we obtain an equivalent instance (G′, k′) of BPVD such that k′ ≤ k, and |V (G′)| + |E(G′)| ≤ kO(1) © Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, and Shaily Verma; licensed under Creative Commons License CC-BY 4.0