If this link can be any help
A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
A minimum vertex cover is a vertex cover with minimal cardinality.
Consider a set of all minimum vertex covers of a given bipartite graph.
our task is to divide all the vertices of the graph into three sets.
A vertex is in set N (“Never”) if there is no minimum vertex cover containing this vertex.
A vertex is in set A (“Always”) if it is a part of every minimum vertex cover of the given graph.
If a vertex belongs neither to N nor to A, it goes to the set E (“Exists”).
How to classify vertices?
I don't understand the variables. I have an edge from maximum matching then I might have both the endpoints of that edge in the vertex cover. But this scheme does not allow this.