Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of specified cycles in bipartite tournaments   For two integers $n\geq 3$ and $2\leq p\leq n$, we denote $D(n,p)$ the
digraph obtained from a directed $n$-cycle by changing the orientations of
$p-1$ consecutive arcs. In this paper, we show that a family of $k$-regular
$(k\geq 3)$ bipartite tournament $BT_{4k}$ contains $D(4k,p)$ for all $2\leq
p\leq 4k$ unless $BT_{4k}$ is isomorphic to a digraph $D$ such that
$(1,2,3,...,4k,1)$ is a Hamilton cycle and $(4m+i-1,i)\in A(D)$ and
$(i,4m+i+1)\in A(D)$, where $1\leq m\leq k-1$.

21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc