Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Branching Rules: Improvements on Independent Set and Vertex Cover in
  Sparse Graphs   We present an $O^*(1.0919^n)$-time algorithm for finding a maximum
independent set in an $n$-vertex graph with degree bounded by 3, which improves
the previously known algorithm of running time $O^*(1.0977^n)$ by Bourgeois,
Escoffier and Paschos [IWPEC 2008]. We also present an $O^*(1.1923^k)$-time
algorithm to decide if a graph with degree bounded by 3 has a vertex cover of
size $k$, which improves the previously known algorithm of running time
$O^*(1.1939^k)$ by Chen, Kanj and Xia [ISAAC 2003].
  Two new branching techniques, \emph{branching on a bottle} and
\emph{branching on a 4-cycle}, are introduced, which help us to design simple
and fast algorithms for the maximum independent set and minimum vertex cover
problems and avoid tedious branching rules.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ