Shannon Fitzpatrick - The isometric path number of a graph

An isometric path is merely any shortest path between two vertices. Inspired by the game of `Cops and Robber' and a result by Aigner & Fromme, the problem is to determine the minimum number of isometric paths required to cover the vertices of a graph. This number has been found exactly for trees and grid graphs. In this talk, I will present these results as well as give a lower bound on this number in terms of the diameter of the graph and its subgraphs.