On the Complexity of Finding a Potential Community

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10236)


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 finding 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 \(n^{1/2-\epsilon }\)-approximable on bipartite graphs and not \(n^{1-\epsilon }\)-approximable on split graphs, while it is polynomial-time solvable on graphs of bounded degree and their complements, graphs of bounded treewidth, planar graphs, \((C_3,C_6)\)-free graphs, threshold graphs, interval graphs and cographs.


Combinatorial optimization Complexity Algorithm Independent set Inapproximability 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 4
  • Thomas Pontoizeau
    • 1
  • Zsolt Tuza
    • 2
    • 3
  1. 1.Université Paris-Dauphine, PSL Research University, CNRS, LAMSADEParisFrance
  2. 2.Alfréd Rényi Institute of Mathematics, Hungarian Academy of SciencesBudapestHungary
  3. 3.Department of Computer Science and Systems TechnologyUniversity of PannoniaVeszprémHungary
  4. 4.Institut Universitaire de FranceParisFrance

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