Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From edge-disjoint paths to independent paths   Let f(k) denote the maximum such that every simple undirected graph
containing two vertices s,t and k edge-disjoint s-t paths, also contains two
vertices u,v and f(k) independent u-v paths. Here, a set of paths is
independent if none of them contains an interior vertex of another. We prove
that f(k)=k if k<3, and f(k)=3 otherwise.

4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th