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Partitioning powers of traceable or hamiltonian graphs

Abstract : A graph G = (V,E) is arbitrarily partitionable (AP) if for any sequence tau = (n_1, ..., n_p) of positive integers adding up to the order of G, there is a sequence of vertex-disjoints subsets of V whose orders are given by tau and which induce connected graphs. If, additionally, for any k, k <= p, of elements of tau we are allowed to prescribe k vertices belonging to the subsets with given size, we say that G is AP+k. We prove that the kth power of every traceable graph of order at least k is AP+(k-1) and that the kth power of every hamiltonian graph of order at least 2k is AP+(2k-1), and these results are tight.
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Submitted on : Saturday, June 1, 2013 - 3:59:03 PM
Last modification on : Saturday, June 25, 2022 - 10:33:39 AM
Long-term archiving on: : Monday, September 2, 2013 - 5:00:34 AM


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  • HAL Id : hal-00687278, version 2



Olivier Baudon, Julien Bensmail, Jakub Przybylo, Mariusz Woźniak. Partitioning powers of traceable or hamiltonian graphs. Theoretical Computer Science, 2014, 520, ⟨hal-00687278v2⟩



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