Every 3-connected, locally connected, claw-free graph is Hamilton-connected
Armen S. Asratian · Journal of Graph Theory · 1996
A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of order p ≥ 4, containing no induced subgraph isomorphic to K1,3, is Hamilton-connected if and only if G is 3-connected. © 1996 John Wiley & Sons, Inc.