Date of Award

8-2014

Level of Access

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Robert Franzosa

Second Committee Member

Andrew Knightly

Third Committee Member

Benjamin Weiss

Abstract

A prominent question of topological graph theory is "what type of surface can a nonplanar graph be embedded into?" This thesis has two main goals. First to provide a necessary background in topology and graph theory to understand the development of an embedding algorithm. The main purpose is developing and proving a direct constructive embedding algorithm that takes as input the graph with a particular order of edges about each vertex. The embedding algorithm will not only determine which compact surface the graph can be embedded into, but also determines the particular embedding of the graph on the surface. The embedding algorithm is then used to investigate surfaces into which trees and a class of the complete bipartite graphs can be embedded. Further, the embedding algorithm is used to investigate non-surface separating graph embeddings.

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