Powers of Hamiltonian paths in interval graphs

We give a simple proof that the obvious necessary conditions for a graph to contain the kth power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We will also discuss covers by powers of paths and analogues of the Hamiltonian completion number. c © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 31–38, 1998

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