A Chvatal-Erdos type condition for pancyclability

Let G be a graph and S a subset of V(G). Let a(S) denote the maximum number of pairwise nonadjacent vertices in the subgraph G(S) of G induced by S. If G(S) is not complete, let K(S) denote the smallest number of vertices separating two vertices of S and K(S) = vertical bar S vertical bar - 1 otherwise. We prove that if alpha(S) <= kappa(S) and vertical bar S vertical bar is large enough (depending on alpha(S)), then G is S-pancyclable, that is contains cycles with exactly p vertices of S for every p, 3 <= p <= vertical bar S vertical bar. (c) 2006 Elsevier B.V. All rights reserved.