Finding dense subgraphs of sparse graphs

Christian Komusiewicz, Manuel Sorge

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations


We investigate the computational complexity of the Densest-k-Subgraph (D k S) problem, where the input is an undirected graph G = (V,E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on D k S by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density μ of the sought subgraph, D k S becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixed-parameter algorithm for D k S with respect to the combined parameter "degeneracy of G and |V| - k". On the negative side, we find that D k S is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for D k S [Cai, Comput. J., 2008] by showing that for every fixed μ, 0 < μ < 1, the problem of deciding whether G contains a subgraph of density at least μ is W[1]-hard with respect to the parameter |V| - k.

Original languageEnglish
Title of host publicationParameterized and Exact Computation - 7th International Symposium, IPEC 2012, Proceedings
Number of pages10
StatePublished - 1 Dec 2012
Externally publishedYes
Event7th International Symposium on Parameterized and Exact Computation, IPEC 2012 - Ljubljana, Slovenia
Duration: 12 Sep 201314 Sep 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7535 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th International Symposium on Parameterized and Exact Computation, IPEC 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


Dive into the research topics of 'Finding dense subgraphs of sparse graphs'. Together they form a unique fingerprint.

Cite this