A More Complicated Hardness Proof for Finding Densest Subgraphs in Bounded Degree Graphs

TL;DR

This paper proves that finding the densest subgraph of a fixed size remains NP-hard even in graphs with maximum degree three, highlighting the problem's computational difficulty in restricted graph classes.

Contribution

The paper establishes NP-hardness of the Densest-Subgraph problem for graphs with maximum degree three, extending known hardness results to bounded degree graphs.

Findings

NP-hardness holds for degree-3 graphs

Densest-Subgraph problem remains computationally difficult in restricted graph classes

Implications for algorithms in bounded degree graph scenarios

Abstract

We consider the Densest-Subgraph problem, where a graph and an integer k is given and we search for a subgraph on exactly k vertices that induces the maximum number of edges. We prove that this problem is NP-hard even when the input graph has maximum degree three.