Definition:Bipartite Graph

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:

• no two vertices in $A$ are adjacent;
• no two vertices in $B$ are adjacent.

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

Examples