Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs

  • Jiong Guo
  • Yash Raj Shrestha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)


We investigate the computational complexity of Disjoint Π-Vertex Deletion. Here, given an input graph G = (V,E) and a vertex set S ⊆ V, called a solution set, whose removal results in a graph satisfying a non-trivial, hereditary property Π, we are asked to find a solution set S′ with |S′| < |S| and S′ ∩ S = ∅. This problem is partially motivated by the “compression task” occurring in the iterative compression technique. The complexity of this problem has already been studied, with the restriction that Π is satisfied by a graph G iff Π is satisfied by each connected component of G [7]. In this work, we remove this restriction and show that, except for few cases which are polynomial-time solvable, almost all other cases of Disjoint Π-Vertex Deletion are \(\mathcal{NP}\)-hard.


Vertex Cover Cluster Graph Black Vertex Hereditary Property Vertex Deletion 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jiong Guo
    • 1
  • Yash Raj Shrestha
    • 1
  1. 1.Universität des SaarlandesSaarbrückenGermany

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