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.

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?"

A 2-partite graph is the same as a bipartite graph.

Since is a bipartite graph, we may consider its adjacency matrix.

In this problem, we are given a bipartite graph with an order on the vertices, and an edge.

The corresponding question "How many perfect matchings does the given bipartite graph have?"

No smaller non-hamiltonian cubic 3-connected bipartite graph is currently known.

A complete bipartite graph K has m n spanning trees.

It is convenient to consider holographic reductions on bipartite graphs.

In any directed bipartite graph, all cycles have a length that is divisible by two.

It consists of finding a maximum weight matching in a weighted bipartite graph.

The algorithm is easier to describe if we formulate the problem using a bipartite graph.

The complete bipartite graph K has edge covering number max(m, n).

The 2-colorable graphs are exactly the bipartite graphs, including trees and forests.

The star K shown in the illustration is a complete bipartite graph, and therefore may be colored with two colors.

The complete bipartite graph has a minimum vertex cover of size .

See Zarankiewicz problem for more on the extremal functions of bipartite graphs.

When modelling relations between two different classes of objects, bipartite graphs very often arise naturally.

Bipartite graphs may be characterized in several different ways:

All complete bipartite graphs which are trees are stars.

Properties 1 and 2 define a bipartite graph.

Clearly, the matrix B uniquely represents the bipartite graphs.