On the Discrete Number of Tree Graphs
| dc.contributor.author | Rhodes, Benjamin Robert | en |
| dc.contributor.committeechair | Palsson, Eyvindur Ari | en |
| dc.contributor.committeemember | Senger, Steven M. | en |
| dc.contributor.committeemember | Fraas, Martin | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2020-05-23T08:00:24Z | en |
| dc.date.available | 2020-05-23T08:00:24Z | en |
| dc.date.issued | 2020-05-22 | en |
| dc.description.abstract | 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. | en |
| dc.description.abstractgeneral | 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. | en |
| dc.description.degree | Master of Science | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:25577 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/98536 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | tree graphs | en |
| dc.subject | distance problem | en |
| dc.subject | bounds | en |
| dc.title | On the Discrete Number of Tree Graphs | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |