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Parameterized Lower Bound and NP-Completeness of Some H-Free Edge Deletion Problems

  • N. R. Aravind
  • R. B. SandeepEmail author
  • Naveen Sivadasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9486)

Abstract

For a graph H, the \(H\)-free Edge Deletion problem asks whether there exist at most k edges whose deletion from the input graph G results in a graph without any induced copy of H. We prove that \(H\)-free Edge Deletion is NP-complete if H is a graph with at least two edges and H has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time \(2^{o(k)}\cdot |G|^{O(1)}\), unless Exponential Time Hypothesis fails.

Keywords

Regular Graph Input Graph Star Graph Edge Deletion Vertex Deletion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • N. R. Aravind
    • 1
  • R. B. Sandeep
    • 1
    Email author
  • Naveen Sivadasan
    • 2
  1. 1.Department of Computer Science & EngineeringIndian Institute of Technology HyderabadHyderabadIndia
  2. 2.TCS Innovation LabsHyderabadIndia

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