Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Melissa Keranen

Committee Member 1

William Keith

Committee Member 2

Fabrizio Zanello

Committee Member 3

Soner Onder


This dissertation tackles the challenging graph decomposition problem of finding solutions to the uniform case of the Hamilton-Waterloo Problem (HWP). The HWP seeks decompositions of complete graphs into cycles of specific lengths. Here, we focus on cases with a single factor of 6-cycles. The dissertation then delves into the construction of 1-rotational designs, a concept from finite geometry. It explores the connection between these designs and finite projective planes, which are specific geometric structures. Finally, the dissertation proposes a potential link between these seemingly separate areas. It suggests investigating whether 1-rotational designs might hold the key to solving unsolved instances of the uniform HWP. By exploring this connection, the research aims to find new constructions and solutions for these long standing open problems.