Every 3-connected claw-free B_{i;7-i}-free graph is Hamiltonian - Saburov, Khikmat; Saburov, Mansoor (Science & Knowledge Publishing Corporation Limited, 2012)
In this paper we have proved that every 3-connected K_{1;3}B_{2;5} (or K_{1;3}B_{3;4})-free graph is Hamiltonian.