Partitioning powers of traceable or hamiltonian graphs.

Abstract: A graph is arbitrarily partitionable (AP) if for any sequence of positive integers adding up to the order of G, there is a sequence of mutually disjoint subsets of V whose sizes are given by τ and which induce connected graphs. If, additionally, for given k, it is possible to prescribe vertices belonging to the first l subsets of τ, G is said to be . The paper contains the proofs that the kth power of every traceable graph of order at least k is and that the kth power of every hamiltonian graph of order at least 2k is , and these results are tight. [Copyright &y& Elsevier]