Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-time Approximation Scheme for Minimum k-cut in Planar and
  Minor-free Graphs   The $k$-cut problem asks, given a connected graph $G$ and a positive integer
$k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$
connected components. We give the first polynomial-time algorithm with
approximation factor $2-\epsilon$ (with constant $\epsilon > 0$) for the
$k$-cut problem in planar and minor-free graphs. Applying more complex
techniques, we further improve our method and give a polynomial-time
approximation scheme for the $k$-cut problem in both planar and minor-free
graphs. Despite persistent effort, to the best of our knowledge, this is the
first improvement for the $k$-cut problem over standard approximation factor of
$2$ in any major class of graphs.

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an