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

 * BipartiteGraphs.png