# How to define a path between two sets of vertices?

In section 17.2 of the book "Combinatorial optimization polyhedra and efficiency" by Schrijver, he describes the Hungarian method for maximum weight matching in bi-partite graphs (with classes $$U$$ and $$W$$). He defines for a matching, $$M$$, $$U_M$$ and $$W_M$$ as the set of vertices in $$U$$ and $$W$$ missed by $$M$$. He then says "if there is a $$U_M - W_M$$ path, find the shortest such path". I'm not sure what this means. How is a path between two sets of vertices defined?

He is describing this path on a directed graph, $$D_M$$ where all edges in $$M$$ are directed from $$U$$ to $$W$$ and edges not in $$M$$ are directed from $$W$$ to $$U$$.

An $$A$$-$$B$$ path is a path that starts at some $$a \in A$$ and ends at some $$b \in B$$.