## Abstract

In the l-PATH VERTEX COVER problem (resp., the l-COMPONENT ORDER CONNECTIVITY problem) the input is an undirected graph G and an integer k. The goal is to decide whether there is a set of vertices of size at most k whose deletion from G results in a graph that does not contain a path with l vertices (resp., does not contain a connected component with at least l vertices). In this paper we give a parameterized algorithm for l-PATH VERTEX COVER when l=5,6,7, whose running times are O^{⁎}(3.945^{k}), O^{⁎}(4.947^{k}), and O^{⁎}(5.951^{k}), respectively. We also give an algorithm for l-COMPONENT ORDER CONNECTIVITY whose running time is O^{⁎}((l−1−ϵ_{l})^{k}) for every l≥4, where ϵ_{l}>0 for every l.

Original language | English |
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Pages (from-to) | 112-123 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 940 |

DOIs | |

State | Published - 9 Jan 2023 |

## Keywords

- Graph algorithms
- Parameterized complexity

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science