Bryant, Darryn E.; Hoffman, D. G.; Rodger, C. A. 5-cycle systems with holes. (English) Zbl 0867.05016 Des. Codes Cryptography 8, No. 1-2, 103-108 (1996). Summary: Recently the generalized Doyen-Wilson problem of embedding a 5-cycle system of order \(u\) in one of order \(v\) was completely solved. However it is often useful to solve the more general problem of the existence of a 5-cycle system of order \(v\) with a hole of size \(u\). In this paper we completely solve this problem. Cited in 1 ReviewCited in 10 Documents MSC: 05B30 Other designs, configurations 05C38 Paths and cycles 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:Doyen-Wilson problem; 5-cycle system; hole PDFBibTeX XMLCite \textit{D. E. Bryant} et al., Des. Codes Cryptography 8, No. 1--2, 103--108 (1996; Zbl 0867.05016) Full Text: DOI References: [1] D. E. Bryant and C. A. Rodger, On the Doyen-Wilson Theorem form-cycle systems,J. Combin. Designs, Vol. 2 (1994) pp. 253-271. · Zbl 0818.05028 · doi:10.1002/jcd.3180020405 [2] D. E. Bryant and C. A. Rodger, The Doyen-Wilson Theorem extended to 5-cycles,J. Combin. Theory Ser. A, Vol. 68 (1994) pp. 218-224. · Zbl 0809.05019 · doi:10.1016/0097-3165(94)90101-5 [3] J. Doyen and R. M. Wilson, Embeddings of Steiner triple systems,Discrete Math, Vol. 5 (1973) pp. 229-239. · Zbl 0263.05017 · doi:10.1016/0012-365X(73)90139-8 [4] D. G. Hoffman and C. A. Rodger, The chromatic index of complete multipartite graphs,J. Graph Theory, Vol. 16 (1992) pp. 159-163. · Zbl 0760.05041 · doi:10.1002/jgt.3190160207 [5] C. A. Rodger, Problems on cycle systems of odd length,Cong. Numer., Vol. 61 (1988) pp. 5-22. · Zbl 0696.05033 [6] E. Mendelsohn and A. Rosa, Embedding maximum packings of triples,Cong. Numer., Vol. 40 (1983) pp. 235-247. · Zbl 0534.05014 [7] G. Stern and A. Lenz, Steiner triple systems with given subspaces; another proof of the Doyen-Wilson theorem,Boll. Un. Mat. Ital. A (5), Vol. 17 (1980) pp. 109-114. · Zbl 0501.05012 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.