Spanning acyclic subdigraphs and strong t-panconnectivity of tournaments

In 1980, C. Thomassen ( 28: 142-163) proved that if a 2-strong semicomplete digraph contains three internally disjoint -paths each of length at least 2, then has a Hamiltonian -path. It follows that every 4-strong tournament is strongly Hamiltonian-connected.In this paper, we prove that if a semicomplete digraph has a spanning acyclic subdigraph from to such that the length of the longest -paths in is , then contains all -paths of lengths at least . By using this new sufficient condition to confirm the strong -panconnectivity in , we prove that if a 2-strong tournament with vertices contains internally disjoint -paths each of length at least 2, then has all -paths of lengths at least . This implies that every -strong tournament is strongly -panconnected.