Routing permutations and 2-1 routing requests in the hypercube

Abstract : Let Hn be the directed symmetric n-dimensional hypercube. Using the computer, we show that for any permutation of the vertices of H4, there exists a system of pairwise arc-disjoint directed paths from each vertex to its target in the permutation. This verifies Szymanski's conjecture for n=4. We also consider the so-called 2-1 routing requests in Hn, where any vertex can be used twice as a source but only once as a target; we construct for any n≥3 a 2-1 request that cannot be routed in Hn by arc-disjoint paths:in other words, for n≥3, Hn is not (2-1)-rearrangeable.
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Contributor : Olivier Baudon <>
Submitted on : Tuesday, December 6, 2011 - 5:43:52 PM
Last modification on : Thursday, April 5, 2018 - 10:36:49 AM

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  • HAL Id : hal-00649005, version 1

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Olivier Baudon, Guillaume Fertin, Ivan Havel. Routing permutations and 2-1 routing requests in the hypercube. Discrete Applied Mathematics, Elsevier, 2001, 113, pp.43-58. ⟨hal-00649005⟩

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