On hamiltonian connectedness of K1,4-free graphs

Abstract

G. Chen and R.H. Schelp proved that every 3-connected K 1,4-free graph G on n vertices with ∑ i=1 3 d( v i )⩾ n+4 for any independent set { v 1, v 2, v 3} of G is hamiltonian connected. In this paper, we show that every 3-connected K 1,4-free graph G∉ J on at most 4 δ−10 vertices is hamiltonian connected, where J is the set of exceptional graphs.