How to define a path between two sets of vertices? In section 17.2 of the book &quot;Combinatorial optimization polyhedra and efficiency&quot; 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 &quot;if there is a $U_M - W_M$ path, find the shortest such path&quot;. 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 $b \in B$.