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.
This work has been funded by grant ANR 2010 BLAN 021902.
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Bougeret, M., Bousquet, N., Giroudeau, R., Watrigant, R. (2014). Parameterized Complexity of the Sparsest k-Subgraph Problem in Chordal Graphs. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_14
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DOI: https://doi.org/10.1007/978-3-319-04298-5_14
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