On equationally defining extended cycle systems Original Research Article

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 ∈ {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.