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On equationally defining m-perfect 2m + 1 cycle systems

✍ 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

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✦ 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.


πŸ“œ SIMILAR VOLUMES


On equationally defining extended cycle
✍ C.C. Lindner; C.A. Rodger πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 654 KB

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

{2, 3}-perfect m-cycle systems are equat
✍ E. M. Li Marzi; C. C. Lindner; F. Rania; R. M. Wilson πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 133 KB

## Abstract An __m__‐cycle system (S__,C__) of order __n__ is said to be {2,3}‐perfect provided each pair of vertices is connected by a path of length 2 in an __m__‐cycle of __C__ and a path of length 3 in an __m__‐cycle of __C__. The class of {2,3}‐perfect __m__‐cycle systems is said to be equatio

2-perfect m-cycle systems
✍ C.C. Lindner; C.A. Rodger πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 530 KB
A partial m=(2k+1)-cycle system of order
✍ C.C. Lindner; C.A. Rodger πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 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).