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)


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.


Regular Graph Input Graph Star Graph Edge Deletion Vertex Deletion 
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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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