Fully cycle extendability of K1,4K1,4-restricted graphs

A subgraph isomorphic to K1,p(p≥3) in a graph GG is a pp-claw   of GG. A graph GG is K1,pK1,p-restricted   if for any pp-claw HH of GG the number of the edges in GG among vertices of degree 1 in HH is at least p−2p−2. Clearly, every claw-free graph is K1,pK1,p-restricted. We prove that every connected, locally connected K1,4K1,4-restricted graph with minimum degree at least 3 is fully cycle extendable.