@inproceedings{b3f84b2d584b4445967f95f885d67280,

title = "Large Independent Sets in Triangle-Free Planar Graphs",

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})}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).",

author = "Zdenek Dvorak and Matthias Mnich",

year = "2014",

doi = "10.1007/978-3-662-44777-2_29",

language = "English",

isbn = "978-3-662-44776-5",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "346--357",

editor = "Schulz, {Andreas S. } and Dorothea Wagner",

booktitle = "Algorithms - ESA 2014",

address = "United States",

}