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})}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 epsilon>0 such that every planar graph of girth at least five on n vertices has an independent set of size at least n/(3-epsilon).
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2013
- DOI:
- 10.48550/arXiv.1311.2749
- arXiv:
- arXiv:1311.2749
- Bibcode:
- 2013arXiv1311.2749D
- Keywords:
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- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics;
- 68R10;
- G.2.2
- E-Print:
- 14 pages, 1 figure