Neighborhood unions and cyclability of graphs Original Research Article

A graph G is said to be cyclable if for each orientation G→ of G, there exists a set S of vertices such that reversing all the arcs of G→ with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n⩾36. In this paper, we show that if for any three independent vertices x1, x2 and x3, |N(x1)∪N(x2)|+|N(x2)∪N(x3)|+|N(x3)∪N(x1)|⩾2n+1, then G is cyclable.