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Small embeddings for partial 5-cycle systems

✍ Scribed by Geoffrey Martin; Thomas A. McCourt

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 277 KB
Volume: 20
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20306

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✦ Synopsis

Abstract

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≥3**u/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

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