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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)

Abstract

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.

Keywords

Vertex Cover Cluster Graph Black Vertex Hereditary Property 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 2014

Authors and Affiliations

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

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