Work

Destroying Densest Subgraphs is Hard

Year: 2025

Type: article

Abstract: We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion : Given a graph G , a budget k and a target density τ ρ , are there k edges ( k vertices) whose removal from G results in a graph where the densest subgraph has density at most τ ρ ? Here, the density of a graph is the number of its edges divided by the number of its vertices. We prove that both problems are polynomial-time solvable on trees and cliques but are NP-complete on planar bipartite graphs and split graphs. From a parameterized point of view, we show that both problems are fixed-parameter tractable with respect to the vertex cover number but W[1]-hard with respect to the solution size. Furthermore, we prove that Bounded-Density Edge Deletion is W[1]-hard with respect to the feedback edge number, demonstrating that the problem remains hard on very sparse graphs.

Source: Journal of Computer and System Sciences

DOI: 10.1016/j.jcss.2025.103635

Authors: Cristina Bazgan, André Nichterlein, Sofia Vazquez Alferez

Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, Lamsade, Université Paris Dauphine-PSL, Technische Universität Berlin

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,610

OpenAlex ID: W4407430587

FWCI:

Cites: 38

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Related to: 10