Degree sum and hamiltonian-connected line graphs.

In 1984, Bauer proposed the problems of determining best possible sufficient conditions on the vertex degrees of a simple graph (or a simple bipartite graph, or a simple triangle-free graph, respectively) G to ensure that its line graph L(G) is hamiltonian. We investigate the problems of determining best possible sufficient conditions on the vertex degrees of a simple graph G to ensure that its line graph L(G) is hamiltonian-connected, and prove the following.