When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2021.23
URN: urn:nbn:de:0030-drops-154065
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15406/
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### A Polynomial Kernel for Bipartite Permutation Vertex Deletion

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### Abstract

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(9^k |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')| ≤ k^{𝒪(1)}.

### BibTeX - Entry

```@InProceedings{kanesh_et_al:LIPIcs.IPEC.2021.23,
author =	{Kanesh, Lawqueen and Madathil, Jayakrishnan and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
title =	{{A Polynomial Kernel for Bipartite Permutation Vertex Deletion}},
booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages =	{23:1--23:18},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-216-7},
ISSN =	{1868-8969},
year =	{2021},
volume =	{214},
editor =	{Golovach, Petr A. and Zehavi, Meirav},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},