Yale Theory Student Seminar: Asaf Etgar, “On the Connectivity and Diameter of Geodetic Graphs”


Abstract: Geodetic Graphs are graphs in which any two vertices are connected by a unique shortest path. In 1962, Ore asked to characterize this fundamental family.of graphs. Despite many attempts, such characterization seems beyond reach. In this talk we present some history of geodetic graphs, some constructions – and a result that, under reasonable assumptions, limits the structure of geodetic graphs – taking another step towards characterization.