Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On conditional connectivity of the Cartesian product of cycles   The conditional $h$-vertex($h$-edge) connectivity of a connected graph $H$ of
minimum degree $ k > h$ is the size of a smallest vertex(edge) set $F$ of $H$
such that $H - F$ is a disconnected graph of minimum degree at least $h.$ Let
$G$ be the Cartesian product of $r\geq 1$ cycles, each of length at least four
and let $h$ be an integer such that $0\leq h\leq 2r-2$. In this paper, we
determine the conditional $h$-vertex-connectivity and the conditional
$h$-edge-connectivity of the graph $G.$ We prove that both these connectivities
are equal to $(2r-h)a_h^r$, where $a_h^r$ is the number of vertices of a
smallest $h$-regular subgraph of $G.$

10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin