Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spanning trees with at most 2 branch vertices in claw - free graphs   In this article, we will prove that if $G$ is a connected claw-free graph and
either $\sigma_6(G)\geq |G|-5$ or $\sigma_7(G)\geq |G|-2$, here $\sigma_k(G)$
is the minimmum degree sum of $k$ independent vertices in $G$, then $G$ has a
spanning tree with at most two branch vertices.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph