Hamiltonian Connected Line Graphs

1 A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton2 path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion3 of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this4 paper, we prove that the line graph of a (t + 4)-edge-connected graph is (t + 2)-hamiltonian-5 connected if and only if it is (t + 5)-connected, and for s 2 every (s + 5)-connected line6 graph is s-hamiltonian-connected.7 Key words hamiltonian-connected, line graph, collapsible.8 AMS Subject Classification(1991): O5C45, O5C40.9

• Type: Conference
• Year: 2007
• Where: ICCS
• Authors: Dengxin Li, Hong-Jian Lai, Yehong Shao, Mingquan Zhan
• Keywords: Applied Computing, Hamilton2 Path, Hamiltonian-connected Graph, ICCS 2007, Line Graph