SIMULTANEOUS Feedback Vertex set: A parameterized perspective

Akanksha Agrawal, Daniel Lokshtanov, Amer E. Mouawad, Saket Saurabh

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

6 Scopus citations


For a family of graphs F, a graph G, and a positive integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex SET, and ODD CYCLE TRANSVERSAL. A graph G = (V,∪αi=1Ei), where the edge set of G is partitioned into α color classes, is called an α-edge-colored graph. A natural extension of the F-DELETION problem to edge-colored graphs is the α-SIMULTANEOUS F-DELETION problem. In the latter problem, we are given an α-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph Gi \ S, where Gi = (V, Ei) and 1 ≤ i ≤ α, is in F. In this work, we study α-SIMULTANEOUS F-DELETION for F being the family of forests. In other words, we focus on the α-SIMULTANEOUS FEEDBACK VERTEX SET (α-SIMFVS) problem. Algorithmically, we show that, like its classical counterpart, α-SIMFVS parameterized by k is fixed-parameter tractable (FPT) and admits a polynomial kernel, for any fixed constant α. In particular, we give an algorithm running in 2O(αk)nO(1) time and a kernel with O(αk3(α+1)) vertices. The running time of our algorithm implies that α-SimFVS is FPT even when α ∈ o(log n). We complement this positive result by showing that for α ∈ O(log n), where n is the number of vertices in the input graph, α-SIMFVS becomes W[1]-hard. Our positive results answer one of the open problems posed by Cai and Ye (MFCS 2014).

Original languageEnglish
Title of host publication33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
EditorsHeribert Vollmer, Nicolas Ollinger
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770019
StatePublished - 1 Feb 2016
Externally publishedYes
Event33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 - Orleans, France
Duration: 17 Feb 201620 Feb 2016

Publication series

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


Conference33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016


  • Edge-colored graphs
  • Feedback Vertex SET
  • Kernel
  • Parameterized complexity

ASJC Scopus subject areas

  • Software


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