Date of Award
2015
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Jeff Dinitz
Second Advisor
Christian Skalka
Abstract
In this paper we extend the study of Heffter arrays and the biembedding of graphs on orientable surfaces first discussed by Archdeacon in 2014. We begin with the definitions of Heffter systems, Heffter arrays, and their relationship to orientable biembeddings through current graphs. We then focus on two specific cases. We first prove the existence of embeddings for every K_(6n+1) with every edge on a face of size 3 and a face of size n. We next present partial results for biembedding K_(10n+1) with every edge on a face of size 5 and a face of size n. Finally, we address the more general question of ordering subsets of Z_n take away {0}. We conclude with some open conjectures and further explorations.
Language
en
Number of Pages
77 p.
Recommended Citation
Mattern, Amelia, "Ordering and Reordering: Using Heffter Arrays to Biembed Complete Graphs" (2015). Graduate College Dissertations and Theses. 341.
https://scholarworks.uvm.edu/graddis/341