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?

Basically, I want to solve this problem

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