Return to search

Ordering and Reordering: Using Heffter Arrays to Biembed Complete Graphs

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.

Identiferoai:union.ndltd.org:uvm.edu/oai:scholarworks.uvm.edu:graddis-1340
Date01 January 2015
CreatorsMattern, Amelia
PublisherScholarWorks @ UVM
Source SetsUniversity of Vermont
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceGraduate College Dissertations and Theses

Page generated in 0.0015 seconds