An extremal connectivity parameter of tournaments Original Research Article

The effects of the vertex push operation (when a vertex is pushed, the direction of each of its incident arcs is reversed) on the connectivity of tournaments are studied. It is shown that there exists an nk such that any tournament with n vertices, n⩾nk, can be made k-connected using pushes, for any k⩾1. These results imply, for example, that sufficiently large tournaments can be made to have an exponential number of Hamiltonian cycles using pushes and can be made Hamiltonian-connected using pushes.