An Ore-type condition for pancyclability

AbstractLet G be a graph of order n and S a subset of V(G). We define G to be S-pancyclable if for every integer l,3⩽l⩽|S|, there exists a cycle in G that contains exactly l vertices of S. We prove that if the degree sum in G of every pair of nonadjacent vertices of S is at least n, then G is either S-pancyclable or else n is even, S=V(G) and G=Kn/2,n/2, or |S|=4, G[S]=K2,2 and the structure of G is well characterized