Small embeddings for partial 5-cycle systems

It has been conjectured that any partial 5-cycle system of order u can be embedded in a 5-cycle system of order v whenever v≥3u/2+1 and v≡1,5 (mod 10). The smallest known embeddings for any partial 5-cycle system of order u is 10u+5. In this paper we significantly improve this result by proving that for any partial 5-cycle system of order u≥255, there exists a 5-cycle system of order at most (9u+146)/4 into which the partial 5-cycle system of order u can be embedded. © 2011 Wiley Periodicals, Inc. J Combin Designs