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Embedding directed and undirected partial cycle systems of index λ > 1

✍ Scribed by C. C. Lindner; C. A. Rodger

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 610 KB
Volume: 1
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180010203

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✦ Synopsis

Recent results have found small embeddings for partial m-cycle systems of order It with A = 1. However, if A> 1 then the best knswn techniques produce embeddings that are often quadratic functions of both m and n a d linear fmctions of A. In this article we obtain embeddings for partial m-cycle systems of order II, & of partial directed nr-cycle systems, for all values of m. These embeddings are in&pedelml of A and linear ie both n and m.

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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).