A diagonally switchable λ-fold 4-cycle system of order n , briefly DS4CS(n, λ), is a λ-fold 4-cycle system in which by replacing each 4-cycle (a, b, c, d) covering pairs ab, bc, cd, da by either of the 4-cycles (a, c, b, d) or (a, b, d, c) another λ-fold 4-cycle system is obtained. In [3]Adams, Bryant, Grannell, and Griggs proved that a DS4CS(n, 1) exists if and only if n ≡ 1 (mod 8), n ≥ 17 with the possible exception of n = 17. In this paper we prove that for lambda ≥ 2 the necessary conditions for the existence of a lambda-fold 4-cycle system of order n are also sufficient for the existence of a DS4CS(n, λ) except for (n, λ) = (5, 2).
Diagonally switchable lambda-fold 4-cycle systems, lambda > 1
LO FARO, Giovanni;TRIPODI, Antoinette
2010-01-01
Abstract
A diagonally switchable λ-fold 4-cycle system of order n , briefly DS4CS(n, λ), is a λ-fold 4-cycle system in which by replacing each 4-cycle (a, b, c, d) covering pairs ab, bc, cd, da by either of the 4-cycles (a, c, b, d) or (a, b, d, c) another λ-fold 4-cycle system is obtained. In [3]Adams, Bryant, Grannell, and Griggs proved that a DS4CS(n, 1) exists if and only if n ≡ 1 (mod 8), n ≥ 17 with the possible exception of n = 17. In this paper we prove that for lambda ≥ 2 the necessary conditions for the existence of a lambda-fold 4-cycle system of order n are also sufficient for the existence of a DS4CS(n, λ) except for (n, λ) = (5, 2).Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
