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Rotational k-cycle systems of order v k; another proof of the existence of odd cycle systems

✍ Scribed by Marco Buratti

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
112 KB
Volume
11
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

We give an explicit solution to the existence problem for 1‐rotational k‐cycle systems of order v < 3__k__ with k odd and v ≠ 2__k__ + 1. We also exhibit a 2‐rotational k‐cycle system of order 2__k__ + 1 for any odd k. Thus, for k odd and any admissible v < 3__k__ there exists a 2‐rotational k‐cycle system of order v. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 433–441, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10061

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