Definition:Bipartite Graph

Definition
A bipartite graph is a graph $G = \struct {V, E}$ 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:
 * no two vertices in $A$ are adjacent

and
 * no two vertices in $B$ are adjacent.

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

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

Also see

 * Definition:Complete Bipartite Graph