Date of Award
2024
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
Abstract
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.
Recommended Citation
Santizo Huerta, Zazil, "ON GRAPH DECOMPOSITIONS AND DESIGNS: EXPLORING THE HAMILTON-WATERLOO PROBLEM WITH A FACTOR OF 6-CYCLES AND PROJECTIVE PLANES OF ORDER 16", Open Access Dissertation, Michigan Technological University, 2024.