Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dominance complex and vertex cover number   The dominance complex $D(G)$ of a simple graph $G = (V,E)$ is the simplicial
complex consisting of subsets of $V$ whose complements are dominating. We show
that the connectivity of $D(G)$ plus $2$ is a lower bound for the vertex cover
number $\tau(G)$.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat