On the parameterized complexity of simultaneous deletion problems

Akanksha Agrawal, R. Krithika, Daniel Lokshtanov, Amer E. Mouawad, M. S. Ramanujan

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

1 Scopus citations

Abstract

For a family of graphs F, an n-vertex 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 (multi) graph G = (V, ?ai=1Ei), where the edge set of G is partitioned into a color classes, is called an a-edge-colored graph. A natural extension of the F-Deletion problem to edge-colored graphs is the Simultaneous (F1, . . ., Fa)-Deletion problem. In the latter problem, we are given an a-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 = a, is in Fi. Recently, a subset of the authors considered the aforementioned problem with F1 = . . . = Fa being the family of all forests. They showed that the problem is fixed-parameter tractable when parameterized by k and a and can be solved in O(2O(ak)) time1. In this work, we initiate the investigation of the complexity of Simultaneous (F1, . . ., Fa)-Deletion with di erent families of graphs. In the process, we obtain a complete characterization of the parameterized complexity of this problem when one or more of the Fis is the class of bipartite graphs and the rest (if any) are forests. We show that if F1 is the family of all bipartite graphs and each of F2 = F3 = . . . = Fa is the family of all forests then the problem is fixed-parameter tractable parameterized by k and a. However, even when F1 and F2 are both the family of all bipartite graphs, then the Simultaneous (F1, F2)-Deletion problem itself is already W[1]-hard.

Original languageEnglish
Title of host publication37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
EditorsSatya Lokam, R. Ramanujam
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770552
DOIs
StatePublished - 1 Jan 2018
Externally publishedYes
Event37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 - Kanpur, India
Duration: 12 Dec 201714 Dec 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume93
ISSN (Print)1868-8969

Conference

Conference37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
Country/TerritoryIndia
CityKanpur
Period12/12/1714/12/17

Keywords

  • Edge-colored graphs
  • Feedback vertex set
  • Odd cycle transversal
  • Parameterized complexity
  • Simultaneous deletion

ASJC Scopus subject areas

  • Software

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