Transversal Greedoids

In a natural way, a new class of set system is defined in terms of transversals of a family of sets. Examination of the structure of these systems reveals that they are in fact examples of strong greedoids (see [2]), namely greedoids which are greedy algorithm compatible, and we call them transversal greedoids. In this paper, such set systems are shown to be characterized by a simple exchange property.