Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatial graph as connected sum of a planar graph and a braid   In this paper we show that every finite spatial graph is a connected sum of a
planar graph, which is a forest, i.e. disjoint union of finite number of trees
and a tangle.
  As a consequence we get that any finite spatial graph is a connected sum of a
planar graph and a braid. Using these decompositions it is not difficult to
find a set of generators and defining relations for the fundamental group of
compliment of a spatial graph in 3-space $\mathbb{R}^3$.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat