Type of Document	Dissertation
Author	Wood, William Edward
URN	etd-07102006-123516
Title	Combinatorial type problems for triangulation graphs
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Phil Bowers Committee Chair Craig Nolder Committee Member Eric Klassen Committee Member Jack Quine Committee Member Lois Hawkes Committee Member Steve Bellenot Committee Member
Keywords	Graph Theory Circle Packing Discrete Conformal Geometry Conformal Type
Date of Defense	2006-07-06
Availability	unrestricted
Abstract The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may be used to solve the combinatorial type problem in a variety of situations, most significantly in graphs with unbounded degree. Other results regarding the type problem are presented along with several examples illustrating the limits of the results.
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