Minimization and parameterized variants of vertex partition problems on graphs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let Π1, Π2, . . ., Πc be graph properties for a fixed integer c. Then, (Π1, Π2, . . ., Πc)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V1, V2, . . ., Vc such that the subgraph induced by Vi satisfies the graph property Πi for every i ∈ {1, 2, . . ., c}. Minimization and parameterized variants of (Π1, Π2, . . ., Πc)-Partition have been studied for several specific graph properties, where the size of the vertex subset V1 satisfying Π1 is minimized or taken as a parameter. In this paper, we first show that the minimization variant is hard to approximate for any nontrivial additive hereditary graph properties, unless c = 2 and both Π1 and Π2 are classes of edgeless graphs. We then give FPT algorithms for the parameterized variant when restricted to the case where c = 2, Π1 is a hereditary graph property, and Π2 is the class of acyclic graphs.

Original languageEnglish
Title of host publication31st International Symposium on Algorithms and Computation, ISAAC 2020
EditorsYixin Cao, Siu-Wing Cheng, Minming Li
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages401-4013
Number of pages3613
ISBN (Electronic)9783959771733
DOIs
Publication statusPublished - 2020 Dec
Event31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, China
Duration: 2020 Dec 142020 Dec 18

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume181
ISSN (Print)1868-8969

Conference

Conference31st International Symposium on Algorithms and Computation, ISAAC 2020
Country/TerritoryChina
CityVirtual, Hong Kong
Period20/12/1420/12/18

Keywords

  • Approximability
  • Feedback vertex set problem
  • Fixed-parameter tractability
  • Graph algorithms
  • Vertex partition problem

ASJC Scopus subject areas

  • Software

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