Large Independent Sets in Subquartic Planar Graphs

  • Matthias MnichEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9627)


By the famous Four Color Theorem, every planar graph admits an independent set that contains at least one quarter of its vertices. This lower bound is tight for infinitely many planar graphs, and finding maximum independent sets in planar graphs is \(\mathsf {NP}\)-hard. A well-known open question in the field of Parameterized Complexity asks whether the problem of finding a maximum independent set in a given planar graph is fixed-parameter tractable, for parameter the “gain” over this tight lower bound. This open problem has been posed many times [4, 8, 10, 13, 17, 20, 31, 32, 35, 38].

We show fixed-parameter tractability of the independent set problem parameterized above tight lower bound in planar graphs with maximum degree at most 4, in subexponential time.


Planar Graph Tree Decomposition Reduction Rule Path Decomposition Color Theorem 
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.



I am indebted to Zdeněk Dvořák for helpful remarks, and an anonymous reviewer who suggested considering treewidth over pathwidth.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Universität BonnBonnGermany

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