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5-cycle systems with holes. (English) Zbl 0867.05016

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.

MSC:

05B30 Other designs, configurations
05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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