Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A note on hamiltonian cycles in $4$-tough $(P_2\cup kP_1)$-free graphs
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc