graf dwudzielny

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.