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Large Independent Sets in Triangle-Free Planar Graphs

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

Abstract

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).

Keywords

Planar Graph Tree Decomposition Parallel Edge Open Interior Fractional Chromatic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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