Approximation algorithm for maximum independent set in planar traingle-free graphs

  • C. E. Veni Madhavan
Session 7 Algorithms And Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 181)


The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.


Planar Graph Vertex Cover Independence Number Adjacency List Inverted List 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • C. E. Veni Madhavan
    • 1
  1. 1.School of AutomationIndian Institute of ScienceBangaloreIndia

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