# Definition:Bipartite Graph

## Definition

A **bipartite graph** is a graph $G = \left({V, E}\right)$ where:

- $V$ is partitioned into two sets $A$ and $B$ such that:
- each edge is incident to a vertex in $A$ and a vertex in $B$.

That is:

and

It is a common practice when illustrating such a graph to draw the vertices in set $A$ in one colour, and those of set $B$ in another.

$G$ can be denoted $G = \left({A \mid B, E}\right)$ to emphasise that $A$ and $B$ partition $V$.

### Partite Set

Let $G = \left({A \mid B, E}\right)$ be a bipartite graph.

Then $A$ and $B$ are called the **partite sets** of the bipartite graph.

## Examples

## Also see

- Results about
**bipartite graphs**can be found here.

## Sources

- 2008: John M. Harris, Jeffry L. Hirst and Michael J. Mossinghoff:
*Combinatorics and Graph Theory*(2nd ed.): $\S 1.1$