Definition:Bipartite Graph

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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:

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 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

BipartiteGraphs.png


Also see

  • Results about bipartite graphs can be found here.


Sources