On the complexity of finding a potential community

Cristina Bazgan, Thomas Pontoizeau, Zsolt Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An independent 2-clique of a graph is a subset of vertices that is an independent set and such that any two vertices inside have a common neighbor outside. In this paper, we study the complexity of find-ing an independent 2-clique of maximum size in several graph classes and we compare its complexity with the complexity of maximum independent set. We prove that this problem is NP-hard on apex graphs, APX-hard on line graphs, not n1 /2−-approximable on bipartite graphs and not-approximable on split graphs, while it is polynomial-time solvable on graphs of bounded degree and their complements, graphs of bounded treewidth, planar graphs, (C3, C6)-free graphs, threshold graphs, interval graphs and cographs.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings
PublisherSpringer Verlag
Pages80-91
Number of pages12
ISBN (Print)9783319575858
DOIs
Publication statusPublished - Jan 1 2017
Event10th International Conference on Algorithms and Complexity, CIAC 2017 - Athens, Greece
Duration: May 24 2017May 26 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10236 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on Algorithms and Complexity, CIAC 2017
CountryGreece
CityAthens
Period5/24/175/26/17

Keywords

  • Algorithm
  • Combinatorial optimization
  • Complexity
  • Inapproximability
  • Independent set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Bazgan, C., Pontoizeau, T., & Tuza, Z. (2017). On the complexity of finding a potential community. In Algorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings (pp. 80-91). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10236 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-57586-5_8