On Finding Separators in Temporal Split and Permutation Graphs

Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Disconnecting two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s, z)-Separation problem is well-known to be polynomial solvable and serves as an important primitive in many applications related to network connectivity. We study the NP-hard Temporal (s, z) -Separation problem on temporal graphs, which are graphs with fixed vertex sets but edge sets that change over discrete time steps. We tackle this problem by restricting the layers (i.e., graphs characterized by edges that are present at a certain point in time) to specific graph classes. We restrict the layers of the temporal graphs to be either all split graphs or all permutation graphs (both being perfect graph classes) and provide both intractability and tractability results. In particular, we show that in general Temporal (s, z) -Separation remains NP-hard both on temporal split and temporal permutation graphs, but we also spot promising islands of fixed-parameter tractability particularly based on parameterizations that measure the amount of “change over time”.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 23rd International Symposium, FCT 2021, Proceedings
EditorsEvripidis Bampis, Aris Pagourtzis
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9783030865924
StatePublished - 1 Jan 2021
Event23rd International Symposium on Fundamentals of Computation Theory, FCT 2021 - Virtual, Online
Duration: 12 Sep 202115 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12867 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Symposium on Fundamentals of Computation Theory, FCT 2021
CityVirtual, Online


  • Connectivity problems
  • Fixed-parameter tractability
  • NP-hardness
  • Special graph classes
  • Temporal graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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