---
title: Finding large and small dense subgraphs
url: https://www.emergentmind.com/papers/0702032
type: paper
arxiv_id: '0702032'
arxiv_url: https://arxiv.org/abs/0702032
published: '2007-02-05'
categories:
- cs.DS
---

# Finding large and small dense subgraphs

## Abstract

We consider two optimization problems related to finding dense subgraphs. The densest at-least-k-subgraph problem (DalkS) is to find an induced subgraph of highest average degree among all subgraphs with at least k vertices, and the densest at-most-k-subgraph problem (DamkS) is defined similarly. These problems are related to the well-known densest k-subgraph problem (DkS), which is to find the densest subgraph on exactly k vertices. We show that DalkS can be approximated efficiently, while DamkS is nearly as hard to approximate as the densest k-subgraph problem.