A Single-Exponential FPT Algorithm for the K4-Minor Cover Problem

  • Eun Jung Kim
  • Christophe Paul
  • Geevarghese Philip
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

Given an input graph G on n vertices and an integer k, the parameterized K4-minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K4-minor free graph or, equivalently, in a graph of treewidth at most 2. The problem can thus also be called Treewidth-2 Vertex Deletion. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can be expressed as Treewidth-t Vertex Deletion problems: t = 0 for Vertex Cover and t = 1 for Feedback Vertex Set. While a single-exponential FPT algorithm has been known for a long time for Vertex Cover, such an algorithm for Feedback Vertex Set was devised comparatively recently. While it is known to be unlikely that Treewidth-t Vertex Deletion can be solved in time co(k)·nO(1), it was open whether the K4-minor cover could be solved in single-exponential FPT time, i.e. in ck·nO(1) time. This paper answers this question in the affirmative.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eun Jung Kim
    • 1
  • Christophe Paul
    • 2
  • Geevarghese Philip
    • 3
  1. 1.CNRS, LAMSADEParisFrance
  2. 2.CNRS, LIRMMMontpellierFrance
  3. 3.MPIISaarbrückenGermany

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