The Complete Solution of the Intersection Problem for Maximum Packings of K_n with Triples

Abstract

In the late 1980's the intersection problem for maximum packings of K_n with triples was solved by Hoffman, Lindner, and Quattrocchi. Their combined results showed that for any n = i mod(6) such that i in { 0, 2, 4, 5} the intersection spectrum is I(n)={0, 1, ..., x}\{x-1, x-2, x-3, x-5} where x is the size of a maximum packing. Each result was formed when all leaves are the same. However, in this thesis we show that if the leaves are not necessarily the same we can eliminate the exceptions {x-1, x-2, x-3, x-5} of the given results. We show that the intersection spectrum for n = i mod(6) such that i in {4, 5} is I(n)={0, 1, ..., x} where x is the size of a maximum packing and I(n)={0, 1, ..., x}\{x-1} for n = j mod(6) such that j in { 0, 2} and n (not equal to) 8; I(8)={0, 1, 2, 3, 4, 5, 8}.