Building large k-cores from sparse graphs
Journal article, Peer reviewed
Published version
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Date
2023Metadata
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- Department of Informatics [985]
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Original version
Journal of computer and system sciences. 2023, 132, 68-88. 10.1016/j.jcss.2022.10.002Abstract
A k-core of a graph G is the maximal induced subgraph in which every vertex has degree at least k. In the Edge k-Core optimization problem, we are given a graph G and integers k, b and p. The task is to ensure that the k-core of G has at least p vertices, by adding at most b edges. While Edge k-Core is known to be computationally hard in general, we show that there are efficient algorithms when the k-core has to be constructed from a sparse graph with some structural properties. Our results are as follows.
• When the input graph is a forest, Edge k-Core is solvable in polynomial time.
• Edge k-Core is fixed-parameter tractable (FPT) when parameterized by the minimum size of a vertex cover in the input graph.
• Edge k-Core is FPT when parameterized by the treewidth of the graph plus k.