An Ore-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 a simple graph of even ordern ≥ 8. In this paper, we show that if the degree sum of any two nonadjacent vertices is not less thann + 1, then G is cyclable and the lower bound is sharp.