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Parameterized Complexity of the Sparsest k-Subgraph Problem in Chordal Graphs

  • Marin Bougeret
  • Nicolas Bousquet
  • Rodolphe Giroudeau
  • Rémi Watrigant
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8327)

Abstract

In this paper we study the Sparsest k-Subgraph problem which consists in finding a subset of k vertices in a graph which induces the minimum number of edges. The Sparsest k-Subgraph problem is a natural generalization of the Independent Set problem, and thus is \({\mathcal NP}\)-hard (and even W[1]-hard) in general graphs. In this paper we investigate the parameterized complexity of both Sparsest k-Subgraph and Densest k-Subgraph in chordal graphs. We first provide simple proofs that Densest k-Subgraph in chordal graphs is FPT and does not admit a polynomial kernel unless \({\mathcal NP} \subseteq co{\mathcal NP}/poly\) (both parameterized by k). More involved proofs will ensure the same behavior for Sparsest k-Subgraph in the same graph class.

Keywords

Parameterized Complexity Interval Graph Polynomial Kernel Tree Decomposition Chordal Graph 
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

  • Marin Bougeret
    • 1
  • Nicolas Bousquet
    • 1
  • Rodolphe Giroudeau
    • 1
  • Rémi Watrigant
    • 1
  1. 1.LIRMMUniversité Montpellier 2France

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