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Embedding partial odd-cycle systems in systems with orders in all admissible congruence classes

✍ Scribed by Daniel Horsley; David A. Pike

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
97 KB
Volume
18
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

For odd m, relatively little is known about embedding partial m‐cycle systems into m‐cycle systems of small orders not congruent to 1 or m modulo 2__m__. In this paper we prove that any partial m‐cycle system of order u can be embedded in an m‐cycle system of order v if v≥m(2__u__+1)+(m−1)/2, v is odd and \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$$\left( {_{2}^{V} } \right) \equiv 0\left( {\bmod {\rm }m} \right)$$\end{document}. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 202–208, 2010

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A partial m=(2k+1)-cycle system of order
A partial m=(2k+1)-cycle system of order n can be embedded in an m-cycle system of order (2n+1)m
✍ C.C. Lindner; C.A. Rodger 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 566 KB

A generalization of Cruse's Theorem on embedding partial idempotent commutative latin squares is developed and used to show that a partial m = (2k + I)-cycle system of order n can be embedded in an m-cycle system of order tm for every odd t 2 (2n + 1).