Craig Larson

*Radius and Independence *

**Abstract**

The *eccentricity* of a vertex *v* in a graph *G* is the maximum distance from *v* to any other vertex of the graph. The *radius* of a connected graph is the minimum eccentricity of any of its vertices. A connected graph is *radius-critical* if the removal of any vertex either disconnects the graph or decreases the radius of the remaining graph. In this talk, an interesting characterization, due to Siemion Fajtlowicz, of radius-critical graphs is discussed, as well as its implications for the structure of any graph, and a conjecture of the program Graffiti (proved by Erdös, Saks, and Sos).