Complexity of Most Vital Nodes for Independent Set in Graphs Related to Tree Structures

  • Cristina Bazgan
  • Sonia Toubaline
  • Zsolt Tuza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


Given an undirected graph with weights on its vertices, the k most vital nodes independent set problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets. We also consider the complementary problem, minimum node blocker independent set that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on graphs of bounded treewidth and cographs. A result on the non-existence of a ptas is presented, too.


most vital nodes independent set complexity NP-hard ptas bipartite graph bounded treewidth cograph 

Mathematics Subject Classification

05C85 05C69 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Cristina Bazgan
    • 1
  • Sonia Toubaline
    • 1
  • Zsolt Tuza
    • 2
    • 3
  1. 1.LAMSADEUniversité Paris-DauphineFrance
  2. 2.Computer and Automation InstituteHungarian Academy of SciencesBudapestHungary
  3. 3.Department of Computer Science and Systems TechnologyUniversity of VeszprémHungary

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