Speaker: Ortrud R. Oellermann
Title: Convexity in Graphs

Abstract:
Abstractions of properties that hold for convex sets in Euclidean space have 
been defined and studied for a variety of structures. In the case of graphs, 
convex sets are usually defined in terms of an `interval' type; the most 
well-known being the shortest path intervals and induced path intervals. 
The respective convexities are referred to as the geodesic and monophonic 
convexities. For a given graph convexity, those properties possessed by 
(closed and bounded) convex sets in Euclidean space do not in general hold 
for the corresponding convex sets. Instead the goal is to find structural 
characterizations of those graphs for which these properties hold.  These 
graphs frequently belong to the class of perfect graphs. We survey results 
that are known for the geodesic and monophonic convexities and discuss more 
recently studied convexities that are defined in terms of Steiner trees and 
minimal trees.