We study a generalization of the problem of finding bounds on the number of discrete chains, which itself is a generalization of the Erdős unit distance problem. Given a set of points in Euclidean space and a tree graph consisting of a much smaller number of vertices, we study the maximum possible number of tree graphs which can be represented by a prescribed tree graph. We derive an algorithm for finding tight bounds for this family of problems up to chain bound discrepancy, and give upper and lower bounds in special cases. / Master of Science / We study a generalization of the problem of finding bounds on the number of discrete chains, which itself is a generalization of the Erdős unit distance problem, a famous mathematics problem named after mathematician Paul Erdős. Given a set of points, and a tree graph of a much smaller amount of vertices, we study the maximum possible number of tree graphs which can be represented by a prescribed tree graph. We derive an algorithm for finding tight bounds for this family of problems up to chain bound discrepancy, and give upper and lower bounds in special cases.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/98536 |
| Date | 22 May 2020 |
| Creators | Rhodes, Benjamin Robert |
| Contributors | Mathematics, Palsson, Eyvindur Ari, Senger, Steven M., Fraas, Martin |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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