Squashing maximum packings of Kn with 8-cycles into maximum packings of Kn with 4-cycles

Abstract

An 8-cycle is said to be squashed if we identify a pair of opposite vertices and name one of them with the other (and thereby turning the 8-cycle into a pair of 4-cycles with exactly one vertex in common). The resulting pair of 4-cycles is called a bowtie. We say that we have squashed the 8-cycle into a bowtie. Evidently an 8-cycle can be squashed into a bowtie in eight different ways. The object of this paper is the construction, for every n > 8, of a maximum packing of Kn with 8-cycles which can be squashed in a maximum packing of Kn with 4-cycles.