## Abstract

In this paper we consider two vertex deletion problems. In the BLOCK VERTEX DELETION problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a block graph (a graph in which every biconnected component is a clique). In the PATHWIDTH ONE VERTEX DELETION problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a graph with pathwidth at most one. We give a kernel for BLOCK VERTEX DELETION with O(k^{3}) vertices and a kernel for PATHWIDTH ONE VERTEX DELETION with O(k^{2}) vertices. Our results improve the previous O(k^{4})-vertex kernel for BLOCK VERTEX DELETION (Agrawal et al., 2016 [1]) and the O(k^{3})-vertex kernel for PATHWIDTH ONE VERTEX DELETION (Cygan et al., 2012 [3]).

Original language | American English |
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Article number | 106493 |

Journal | Information Processing Letters |

Volume | 186 |

DOIs | |

State | Published - 1 Aug 2024 |

## Keywords

- Algorithms
- Graph algorithms
- Kernelization
- Parameterized complexity

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications