A fan-type condition for cyclability

A graph G is said to be cyclable if for each orientation D of G, there exists a set S(D)⊆V(G) such that reversing all the arcs with one end in S results in a hamiltonian digraph. Let G be 4-connected simple graph of even order n⩾14. In this paper, we show that if max{d(u),d(v)}⩾(n+1)/2 for any u,v∈V(G) with d(u,v)=2, then G is cyclable.