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Partitionable perfect cycle systems with cycle lengths 6 and 8. (English) Zbl 0849.05014

Spectra for existence of \(i\)-perfect \(m\)-cycle systems are studied. The main contributions are for \((i, m)= (2, 6), (2, 8)\) and \((3, 8)\). In each case, existence results for partitionable cycle systems are also obtained.

MSC:

05B30 Other designs, configurations
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[1] Adams, P.; Billington, E. J., The spectrum for 2-perfect 8-cycle systems, Ars Combin., 36, 47-56 (1993) · Zbl 0793.05017
[2] Brouwer, A. E., Optimal packings of \(K_4\)’s into a \(K_n\), J. Combin. Theory Ser. A, 26, 278-297 (1979) · Zbl 0412.05030
[3] D.E. Bryant, A special class of nested Steiner triple systems, Discrete Math., to appear.; D.E. Bryant, A special class of nested Steiner triple systems, Discrete Math., to appear. · Zbl 0851.05023
[4] Hwang, F. K.; Lin, S., Neighbor designs, J. Combin. Theory Ser. A, 23, 302-313 (1977) · Zbl 0405.05017
[5] Keedwell, A. D., Circuit designs and latin squares, Ars Combin., 17, 79-90 (1984) · Zbl 0549.05013
[6] Lindner, C. C., Graph decompositions and quasigroup identities, (Proc. Second Internat. Catania Combinatorial Conf., “Graphs, designs and combinatorial geometries”, Universita di Catania. Proc. Second Internat. Catania Combinatorial Conf., “Graphs, designs and combinatorial geometries”, Universita di Catania, Catania, Sicily, September 4-9, 1989 (1990)), 83-118, a journal version is available in Le Matematiche XLV · Zbl 0735.05065
[7] Lindner, C. C.; Phelps, K. T.; Rodger, C. A., The spectrum for 2-perfect 6-cycle systems, J. Combin. Theory Ser. A, 57, 76-85 (1991) · Zbl 0758.05015
[8] Lindner, C. C.; Rodger, C. A., Decomposition into Cycles II: Cycle Systems, (Dinitz, J. H.; Stinson, D. R., Contemporary Design Theory: a Collection of Surveys (1992), Wiley: Wiley New York), 325-369 · Zbl 0774.05078
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