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

Marin Bougeret, Nicolas Bousquet, Rodolphe Giroudeau, Rémi Watrigant
2014 Lecture Notes in Computer Science  
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 N P-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
more » ... ordal graphs is FPT and does not admit a polynomial kernel unless N P ⊆ coN P/poly (both parameterized by k). More involved proofs will ensure the same behavior for Sparsest k-Subgraph in the same graph class. We lastly provide an F P T algorithm in interval graphs for Sparsest k-Subgraph, but parameterized by the number of edges of the solution (a stronger parameterization than by k).
doi:10.1007/978-3-319-04298-5_14 fatcat:l7z47o7txjfdte4nq3tvjeejvu