Large Independent Sets in Triangle-Free Planar Graphs

  • Zdeněk Dvořák
  • Matthias Mnich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)


Every triangle-free planar graph on n vertices has an independent set of size at least (n + 1)/3, and this lower bound is tight. We give an algorithm that, given a triangle-free planar graph G on n vertices and an integer k ≥ 0, decides whether G has an independent set of size at least (n + k)/3, in time \(2^{O(\sqrt{k})}n\). Thus, the problem is fixed-parameter tractable when parameterized by k. Furthermore, as a corollary of the result used to prove the correctness of the algorithm, we show that there exists ε > 0 such that every planar graph of girth at least five on n vertices has an independent set of size at least n/(3 − ε).


Planar Graph Tree Decomposition Parallel Edge Open Interior Fractional Chromatic Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Zdeněk Dvořák
    • 1
  • Matthias Mnich
    • 2
  1. 1.Computer Science InstituteCharles UniversityPragueCzech Republic
  2. 2.Cluster of Excellence MMCISaarbrückenGermany

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