On ss-hamiltonian-connected line graphs

A graph GG is hamiltonian-connected if any two of its vertices are connected by a Hamilton path (a path including every vertex of GG); and GG is ss-hamiltonian-connected if the deletion of any vertex subset with at most ss vertices results in a hamiltonian-connected graph. In this paper, we prove that the line graph of a (t+4)(t+4)-edge-connected graph is (t+2)(t+2)-hamiltonian-connected if and only if it is (t+5)(t+5)-connected, and for s⩾2s⩾2 every (s+5)(s+5)-connected line graph is ss-hamiltonian-connected.