Hamiltonian paths in spanning subgraphs of line graphs

The line graph is a very popular research object in graph theory, in complex networks and also in social networks recently. In this paper, we show that if a line graph is Hamiltonian-connected, then the graphs in a special family of spanning subgraphs of the line graph are still Hamiltonian-connected. As an important corollary we prove that there exist at least max{1,⌊18δ(G)⌋−1} edge-disjoint Hamiltonian paths between any two vertices in a Hamiltonian-connected line graph L(G).