On hamiltonian connectedness of K1,4-free graphs

G. Chen and R.H. Schelp proved that every 3-connected K1,4-free graph G on n vertices with ∑i=13d(vi)⩾n+4 for any independent set {v1,v2,v3} of G is hamiltonian connected. In this paper, we show that every 3-connected K1,4-free graph G∉J on at most 4δ−10 vertices is hamiltonian connected, where J is the set of exceptional graphs.