Length-bounded cuts: Proper interval graphs and structural parameters

Matthias Bentert, Klaus Heeger, Dušan Knop

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)21-43
Number of pages23
JournalJournal of Computer and System Sciences
Volume126
DOIs
StatePublished - 1 Jun 2022
Externally publishedYes

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

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