Cycles and paths in bipartite tournaments with spanning configurations (Q1823256)

Let T be a bipartite tournament. A spanning subgraph F of T is called a factor of T if \(d^+_ F(x)=1=d^-_ F(x)\) for all \(x\in V(T)\). In this paper, the authors prove that any bipartite tournament T is Hamiltonian if and only if T is strong and has a factor. They also give necessary and sufficient conditions in terms of connectivity and factors for the existence of Hamiltonian path in T. Moreover, the authors conjecture that in k-strongly connected bipartite tournament any k vertices are on a common cycle and prove this for \(k=2\).