Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A Simple Proof of Sharkovsky's Theorem   In this note, we present a simple directed graph proof of Sharkovsky's
theorem.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn