Rhodes, Benjamin Robert2020-05-232020-05-232020-05-22vt_gsexam:25577http://hdl.handle.net/10919/98536We 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.ETDIn Copyrighttree graphsdistance problemboundsThesis