# A polynomial kernel for vertex deletion into bipartite permutation graphs

A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines ℓ_1 and ℓ_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^99) vertices.

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