Hamiltonian-connected tournaments

We characterize weakly Hamiltonian-connected tournaments and weakly panconnected tournaments completely and we apply these results to cycles and bypasses in tournaments with given irregularity, in particular, in regular and almost regular tournaments. We give a sufficient condition in terms of local and global connectivity for a Hamiltonian path with prescribed initial and terminal vertex. From this result we deduce that every 4-connected tournament is strongly Hamiltonian-connected and that every edge of a 3-connected tournament is contained in a Hamiltonian cycle of the tournament and we describe infinite families of tournaments demonstrating that these results are best possible.