## Abstract

We study the LENGTH-BOUNDED CUT problem for special graph classes and from a parameterized complexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set F of at most β edges such that each s-t-path of length at most λ in G contains some edge in F. Bazgan et al. [20] conjectured that LENGTH-BOUNDED CUT admits a polynomial-time algorithm if the input graph is a proper interval graph. We confirm this conjecture by providing a dynamic-programming-based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [15] for LENGTH-BOUNDED CUT parameterized by pathwidth by showing W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that LENGTH-BOUNDED CUT is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms.

Original language | English |
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Pages (from-to) | 21-43 |

Number of pages | 23 |

Journal | Journal of Computer and System Sciences |

Volume | 126 |

DOIs | |

State | Published - 1 Jun 2022 |

Externally published | Yes |

## Keywords

- Edge-disjoint paths
- Feedback vertex number
- Pathwidth

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics