Approximating the Sparsest k-Subgraph in Chordal Graphs

  • Rémi Watrigant
  • Marin Bougeret
  • Rodolphe Giroudeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8447)


Given a simple undirected graph G = (V, E) and an integer k < |V|, the Sparsest k -Subgraph problem asks for a set of k vertices which induces the minimum number of edges. As a generalization of the classical independent set problem, Sparsest k -Subgraph is \(\mathcal{NP}\)-hard and even not approximable unless \(\mathcal{P} = \mathcal{NP}\) in general graphs. Thus, we investigate Sparsest k -Subgraph in graph classes where independent set is polynomial-time solvable, such as subclasses of perfect graphs. Our two main results are the \(\mathcal{NP}\)-hardness of Sparsest k -Subgraph on chordal graphs, and a greedy 2-approximation algorithm. Finally, we also show how to derive a PTAS for Sparsest k -Subgraph on proper interval graphs.


Interval Graph Chordal Graph Graph Class Perfect Graph Split Graph 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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