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)


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.


Parameterized Complexity Interval Graph Polynomial Kernel Tree Decomposition Chordal Graph 
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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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