This Is AuburnElectronic Theses and Dissertations

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

Date

2020-05-11

Author

Cortez, Joseph

Type of Degree

PhD Dissertation

Department

Mathematics and Statistics

Restriction Status

EMBARGOED

Restriction Type

Full

Date Available

05-08-2022

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).