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Journal Articles Theoretical Computer Science Year : 2014

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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Dates and versions

hal-00687278 , version 1 (12-04-2012)
hal-00687278 , version 2 (01-06-2013)

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  • HAL Id : hal-00687278 , version 2

Cite

Olivier Baudon, Julien Bensmail, Jakub Przybylo, Mariusz Woźniak. Partitioning powers of traceable or hamiltonian graphs. Theoretical Computer Science, 2014, 520, http://www.journals.elsevier.com/theoretical-computer-science/. ⟨hal-00687278v2⟩

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