Lai, Shao and Zhan (J Graph Theory 48:142-146, 2005) showed that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of G is Hamiltonian. It is best possible in some sense. © 2013 Springer Japan.
Tian, R., Xiong, L., & Niu, Z. (2014). On Hamiltonicity of 3-Connected Claw-Free Graphs. Graphs and Combinatorics, 30(5), 1261–1269. https://doi.org/10.1007/s00373-013-1343-7