  Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs,
Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$
for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$.
In this paper, we study the existence of a hamiltonian path in $L^n(G)$, and
give a characterization of $G$ for which $L^n(G)$ has a hamiltonian path. As
applications, we use this characterization to give several upper bounds on the
hamiltonian path index of a graph.
