Hamilton Circuits in the Directed Butterfly Network

Jean-Claude Bermond 1 Eric Darrot Olivier Delmas Stéphane Pérennes
1 SLOOP - Simulation, Object Oriented Languages and Parallelism
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : In this paper, we prove that the wrapped Butterfly digraph $\vec{{\cal WBF}}(d,n)$ of degree $d$ and dimension $n$ contains at least $d-1$ arc-disjoint Hamilton circuits, answering a conjecture of D. Barth. We also conjecture that $\vec{{\cal WBF}}(d,n)$ can be decomposed into $d$ Hamilton circuits, except for $d=2$ $n=2$, $d=2$ $n=3$ and $d=3$ $n=2$ . We show that it suffices to prove the conjecture for $d$ prime and $n=3D2$. Then, we give such a Hamilton decomposition for all primes less than 12000 by a clever computer search, and so, as corollary, we have a Hamilton decomposition of $\vec{{\cal WBF}}(d,n)$ for any $d$ divisible by a number $q$, with $4 \leq q \leq 12000$.
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RR-2925, INRIA. 1996
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Jean-Claude Bermond, Eric Darrot, Olivier Delmas, Stéphane Pérennes. Hamilton Circuits in the Directed Butterfly Network. RR-2925, INRIA. 1996. 〈inria-00073773〉

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