Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the separatrix graph of a rational vector field on the Riemann sphere   We consider the rational flow $\xi_R(z)= R(z) (d/dz)$ where $R$ is given by
the quotient of two polynomials without common factors on the Riemann sphere.
The separatrix graph $\Gamma_R$ is the boundary between trajectories with
different properties. We characterize the properties of a planar directed graph
to be homeomorphic to the separatrix graph of a rational vector field on the
Riemann sphere.

25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
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
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess