The Intersection Problem for Maximum Packings of the Complete Graph with 4-Cycles

Abstract

A maximum packing of K_n with 4-cycles may leave some edges of the graph unpacked. The size of the leave is determined by the congruence class of n modulo 8. When n ≡ 1 (mod 8) the packing coincides with a 4-cycle system of K_n. Billington (J. Combin. Des. 1 (1993) 435-452) has solved the intersection problem for 4-cycle systems. In this dissertation we complete the solution for maximum packings with 4-cycles by solving the cases where n 6≡ 1 (mod 8).