Let G be a 2(k + I)-connected graph of order n. It is proved that if uv rJ. E(G) implies that max{d(u), d(v)} ?: ~ + 2k then G contains k + 1 pairwise disjoint Hamiltonian cycles when c5 (G) ?: 4k + 3. 1 . . Introduction All graphs we consider are finite and simple. We use standard terminology and notation from Bondy and Murty [2] except as indicated. Let G = (V(G), E(G)) be a graph with vertex set V(G) and edge set E(G). For a subset U of V(G), G[U] is the subgraph of G induced by U. For two

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... sjoint subsets (resp. subgraphs) S, T of V(G) (resp. G), put