Large Independent Sets in Triangle-Free Planar Graphs

Zdenek Dvorak*, Matthias Mnich

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

6 Citations (Web of Science)


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})}n2^{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 e > 0 such that every planar graph of girth at least five on n vertices has an independent set of size at least n/(3 - e).
Original languageEnglish
Title of host publicationAlgorithms - ESA 2014
Subtitle of host publication22nd Annual European Symposium Wroclaw, Poland, September 8-10, 2014 Proceedings
EditorsAndreas S. Schulz, Dorothea Wagner
ISBN (Electronic)978-3-662-44777-2
ISBN (Print)978-3-662-44776-5
Publication statusPublished - 2014
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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