On the parameterized complexity of computing graph bisections

René Van Bevern, Andreas Emil Feldmann, Manuel Sorge, Ondřej Suchý

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

11 Scopus citations


The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that Bisection is FPT w.r.t. the minimum cut size if there is an optimum bisection that cuts into a given constant number of connected components. Our algorithm applies to the more general Balanced Biseparator problem where vertices need to be removed instead of edges. We prove that this problem is W[1]-hard w.r.t. the minimum cut size and the number of cut out components. For Bisection we further show that no polynomial-size kernels exist for the cut size parameter. In fact, we show this for all parameters that are polynomial in the input size and that do not increase when taking disjoint unions of graphs. We prove fixed-parameter tractability for the distance to constant cliquewidth if we are given the deletion set. This implies fixed-parameter algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783642450426
StatePublished - 1 Jan 2013
Externally publishedYes
Event39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013 - Lubeck, Germany
Duration: 19 Jun 201321 Jun 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8165 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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