Revisiting the Intersection Problem for Maximum Packings of K_(6n+5) with Triples

Abstract

In 1989, Gaetano Quattrocchi gave a complete solution of the intersection problem for maximum packings of K_(6n+5) with triples when the leave (a 4--cycle) is the same in each maximum packing. Quattrocchi showed that I[2]=2 and I[n]={0, 1, 2, ..., ((n choose 2)-4)/(3) = x \ {x-1, x-2, x-3, x-5} for all n=5 (mod 6)>5. We extend this result by removing the exceptions {x-1, x-2, x-3, x-5} when the leaves are not necessarily the same. In particular, we show that I[n]={0, 1, 2, ..., ((n choose 2)-4)/(3) for all n=5 (mod 6).