Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Independent Sets in Triangle-Free Planar Graphs   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).

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph