Outside perfect 8-cycle systems

Abstract

The two 4-cycles (a, b, c, d) and (e, f, g, h) are called the outside 4-cycles of the 8-cycle (a, b, c, d, e, f, g, h). Given an 8-cycle system, if we can form a 4-cycle system by choosing two outside 4-cycles from each 8-cycle in the system, then the 8-cycle system is called outside perfect. In this paper we prove that an outside perfect maximum packing of K-n with 8-cycles of order n exists for all n >= 8, except n = 9, for which no such system exists.