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Hamilton circuits in the directed wrapped Butterfly network. (English) Zbl 0901.05062
The authors prove that the wrapped Butterfly digraph of outdegree \(d\) and dimension \(n\) contains at least \(d-1\) arc-disjoint Hamilton directed cycles. They conjecture there is a Hamilton decomposition in all cases other than \(d=n=2\); \(d=2\) and \(n=3\); and \(d=3\) and \(n=2\). They offer strong evidence in support of the conjecture. Helen Verrall recently has completed the proof of the conjecture (Discrete Appl. Math., to appear).

MSC:
05C45 Eulerian and Hamiltonian graphs
05C20 Directed graphs (digraphs), tournaments
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
90B18 Communication networks in operations research
05C38 Paths and cycles
05C90 Applications of graph theory
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