On the Discrete Number of Tree Graphs

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2020

Author dc:creator

• Rhodes, Benjamin Robert

Chair dc:contributor.committeechair

• Palsson, Eyvindur Ari

Committee members dc:contributor.committeemember

• Senger, Steven M.
• Fraas, Martin

• tree graphs
• distance problem
• bounds

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:25577

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/98536