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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 τ =(n1,...,np) 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 l = min{k, p} vertices belonging to the first l subsets of τ, G is said to be AP+k. The paper contains the proofs 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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https://hal.archives-ouvertes.fr/hal-00919048
Contributor : Olivier Baudon Connect in order to contact the contributor
Submitted on : Monday, December 16, 2013 - 11:37:24 AM
Last modification on : Saturday, June 25, 2022 - 10:34:18 AM

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Olivier Baudon, Julien Bensmail, Jakub Przybylo, Mariusz Woźniak. Partitioning powers of traceable or hamiltonian graphs. Theoretical Computer Science, 2014, 520, http://dx.doi.org/10.1016/j.tcs.2013.10.016. ⟨10.1016/j.tcs.2013.10.016⟩. ⟨hal-00919048⟩

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