On s-hamiltonian-connected line graphs

A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this paper, we prove that the line graph of a (t + 4)-edge-connected graph is (t + 2)-hamiltonian-connected if and only if it is (t + 5)-connected, and for s 2 every (s + 5)-connected line graph is s-hamiltonian-connected. Published by Elsevier B.V. MSC: O5C45; O5C40

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Hong-Jian Lai, Yanting Liang, Yehong Shao
• Keywords: DM 2008, Hamilton Path, Hamiltonian-connected Graph, Line Graph