Discrete Mathematics and Combinatorics Commons^™

On Graph Decompositions And Designs: Exploring The Hamilton-Waterloo Problem With A Factor Of 6-Cycles And Projective Planes Of Order 16, Zazil Santizo Huerta

Dissertations, Master's Theses and Master's Reports

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 …