An example of bipartite graph is a job matching problem.
In a weighted bipartite graph, each edge has an associated value.
This is a special subdivision, as it always results in a bipartite graph.
In this problem, we are given a bipartite graph with an order on the vertices, and an edge.
How many perfect matchings are there for a given bipartite graph?
It was known before that the decision problem "Is there a perfect matching for a given bipartite graph?"
The corresponding question "How many perfect matchings does the given bipartite graph have?"
The algorithm is easier to describe if we formulate the problem using a bipartite graph.
A 2-partite graph is the same as a bipartite graph.
Since is a bipartite graph, we may consider its adjacency matrix.
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