Adams, Peter; Billington, Elizabeth J.; Bryant, Darryn E. Partitionable perfect cycle systems with cycle lengths 6 and 8. (English) Zbl 0849.05014 Discrete Math. 149, No. 1-3, 1-9 (1996). 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. Reviewer: C.J.Colbourn (Waterloo/Ontario) Cited in 1 ReviewCited in 4 Documents MSC: 05B30 Other designs, configurations Keywords:\(m\)-cycle systems; partitionable cycle systems PDFBibTeX XMLCite \textit{P. Adams} et al., Discrete Math. 149, No. 1--3, 1--9 (1996; Zbl 0849.05014) Full Text: DOI References: [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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.