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

Marin Bougeret 1 Nicolas Bousquet 2 Rodolphe Giroudeau 1 Rémi Watrigant 1
1 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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 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 NP⊆coNP/poly (both parameterized by k). More involved proofs will ensure the same behavior for Sparsest k-Subgraph in the same graph class.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01251025
Contributor : Rodolphe Giroudeau <>
Submitted on : Tuesday, January 5, 2016 - 3:15:05 PM
Last modification on : Friday, May 3, 2019 - 12:08:04 PM

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Marin Bougeret, Nicolas Bousquet, Rodolphe Giroudeau, Rémi Watrigant. Parameterized Complexity of the Sparsest k-Subgraph Problem in Chordal Graphs. SOFSEM: Theory and Practice of Computer Science, Jan 2014, Nový Smokovec, Slovakia. pp.150-161, ⟨10.1007/978-3-319-04298-5_14⟩. ⟨lirmm-01251025⟩

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