Diagonally switchable 4-cycle systems

Adams, P.; Bryant, D.; Grannell, Mike and Griggs, Terry (2006). Diagonally switchable 4-cycle systems. Australasian Journal of Combinatorics, 34, pp. 145–152.

Abstract

A diagonally switchable 4-cycle system of order $n$, briefly DS4CS($n$), is a 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 4-cycle system is obtained. We prove that a DS4CS($n$) exists if and only if $n \equiv$ 1 (mod 8), $n \geq 17$ with the possible exception of $n = 17$.

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