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Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs

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Algorithms and Computation (WALCOM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8344))

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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.

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Authors and Affiliations

  1. Universität des Saarlandes, Campus E 1.7, 66123, Saarbrücken, Germany

    Jiong Guo & Yash Raj Shrestha

Authors
  1. Jiong Guo
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  2. Yash Raj Shrestha
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Sudebkumar Prasant Pal

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, 101-8430, Chiyoda-ku, Tokyo, Japan

    Kunihiko Sadakane

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Guo, J., Shrestha, Y.R. (2014). Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_27

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  • DOI: https://doi.org/10.1007/978-3-319-04657-0_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04656-3

  • Online ISBN: 978-3-319-04657-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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