On the existence of specified cycles in bipartite tournaments

For two integers $n\ge 3$ and $2\le p\le n$, 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 $(k\ge 3)$ bipartite tournament $B{T}_{4k}$ contains $D(4k,p)$ for all $2\leq p\leq 4k$unless$BT_{4k}$isisomorphictoadigraph$D$suchthat$(1,2,3,…,4k,1)$isaHamiltoncycleand$(4m+i-1,i)\in A(D)$and$(i,4m+i+1)\in A(D)$,where$1\leq m\leq k-1$.