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
On equationally defining m-perfect 2m + 1 cycle systems
β Scribed by C. C. Lindner; C. A. Rodger
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 434 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
In this article we give a complete solution to the problem of equationally defining m-perfect (2m + 1)-cycle systems and of equationally defining rn-perfect directed (2m + 1)-cycle systems.
π SIMILAR VOLUMES
## Abstract An __m__βcycle system (S__,C__) of order __n__ is said to be {2,3}βperfect provided each pair of vertices is connected by a path of length 2 in an __m__βcycle of __C__ and a path of length 3 in an __m__βcycle of __C__. The class of {2,3}βperfect __m__βcycle systems is said to be equatio
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).