zbMATH — the first resource for mathematics

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).

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
Full Text: DOI Link
[1] Alspach, B., Research problem 59, Discrete math., 50, 115, (1984)
[2] Alspach, B.; Bermond, J-C.; Sotteau, D., Decomposition into cycles I: Hamilton decompositions, (), 9-18 · Zbl 0713.05047
[3] Aubert, J.; Schneider, B., Décomposition de la somme cartésienne d’un cycle et de l’union de deux cycles en cycles hamiltoniens, Discrete math., 38, 7-16, (1982) · Zbl 0475.05057
[4] R. Balakrishnan, J.C. Bermond, P. Paulraja, On the decomposition of de Bruijn graphs into hamiltonian cycles, manuscript.
[5] Barm, D., Réseaux d’interconnection: structures et communications, ()
[6] Barth, D.; Bond, J.; Raspaud, A., Compatible Eulerian circuits in \(K\^{}\{∗∗\}n\), Discrete appl. math., 56, 127-136, (1995) · Zbl 0877.05032
[7] Barth, D.; Raspaud, A., Two edge-disjoint Hamiltonian cycles in the butterfly graph, Inform. process. lett., 51, 175-179, (1994) · Zbl 0807.05047
[8] Bermond, J-C.; Darrot, E.; Delmas, O.; Perennes, S., Hamilton cycle decomposition of the butterfly network, (), (to appear) · Zbl 0901.05062
[9] Bermond, J.-C.; Favaron, O.; Maheo, M., Hamiltonian decomposition of Cayley graphs of degree 4, J. combin. theory ser. B, 46, 2, 142-153, (1989) · Zbl 0618.05032
[10] Bermond, J-C.; Peyrat, C., Broadcasting in de Bruijn networks, (), 283-292, Florida · Zbl 0673.94027
[11] S.J. Curran, J.A. Gallian, Hamilton cycles and paths in Cayley graphs and digraphs — a survey, Discrete Math. (to appear). · Zbl 0857.05067
[12] Fleischner, H.; Jackson, B., Compatible Euler tours in Eulerian digraphs, (), 95-100 · Zbl 0743.05036
[13] Leighton, F.T., Introduction to parallel algorithms and architectures: arrays. trees. hypercubes, () · Zbl 0743.68007
[14] Rowley, R.; Bose, B., On the number of arc-disjoint Hamiltonian circuits in the de Bruijn graph, Parallel process. lett., 3, 375-380, (1993)
[15] De Rumeur, Jean, Communication dans LES réseaux de processeurs, (), (English version to appear)
[16] Syska, M., Communications dans LES architectures à mémoire distribuée, ()
[17] Tillson, T., A Hamiltonian decomposition of \(K\^{}\{∗\}2m\), 2m ⩾ 8, J. combin. theory ser. B, 29, 68-74, (1980) · Zbl 0439.05025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.