✦ LIBER ✦

On equationally defining extended cycle systems

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

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 654 KB
Volume: 173
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00136-7

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✦ Synopsis

It has been previously shown by Bryant and Lindner that the only values of m for which 2-perfect m-cycle systems can be equationally defined are m e {3, 5,7}. In this paper more general graph decompositions of an m-cycle system are defined, namely extended cycle systems, and it is shown that if m is odd then extended m-cycle systems can be equationally defined if and only if m ~ {3, 5, 7}. The equations used to define the extended cycle systems are the same as those for cycle systems except that the idempotent law no longer applies.

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