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Article Dans Une Revue Discrete Applied Mathematics Année : 1998

Hamilton circuits in the directed wrapped Butterfly network

Résumé

In this paper, we prove that the wrapped Butterfly digraph WBF(d, n) of degree d and dimension n contains at least d − 1 arc-disjoint Hamilton circuits, answering a conjecture of Barth [5]. We also conjecture that WBF(d, n) can be decomposed into d Hamilton circuits, except for {d = 2 and n = 2}, {d = 2 and n = 3} and {d = 3 and n = 2}. We show that it suffices to prove this conjecture for d prime and n = 2. Then, we give such a Hamilton decomposition for all primes to 12000 by a clever computer search, and so, as a corollary, we have a Hamilton decomposition of (d, n) for any d divisible by a number q, with 4 ⩽ q ⩽ 12000.
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Dates et versions

hal-00407356 , version 1 (27-09-2022)

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Jean-Claude Bermond, Eric Darrot, Olivier Delmas, Stéphane Pérennes. Hamilton circuits in the directed wrapped Butterfly network. Discrete Applied Mathematics, 1998, 84 (1-3), pp.21-42. ⟨10.1016/S0166-218X(97)00095-4⟩. ⟨hal-00407356⟩
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