  We define and study greedy matchings in vertex-ordered bipartite graphs. It
is shown that each vertex-ordered bipartite graph has a unique greedy matching.
The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a
preference relation. Given a vertex-ordered bipartite graph, the goal is to
match every vertex of one vertex class but to leave unmatched as many as
possible vertices of low preference in the other concept class. We investigate
how well greedy algorithms perform in this setting. It is shown that they have
optimal performance provided that the vertex-ordering is cleverly chosen. The
study of greedy matchings is motivated by problems in learning theory like
illustrating or teaching concepts by means of labeled examples.
