Cyclability in kk-connected K1,4K1,4-free graphs

It is proved that if GG is a kk-connected K1,4K1,4-free graph and SS is a subset of vertices such that k≥3k≥3 and |S|≤2k|S|≤2k then GG has a cycle containing SS. A similar result is obtained when restricting the kk-connectivity assumption to the subset SS.